Communications in Mathematical Biology and Neuroscience (CMBN) is a peer-reviewed open access international journal, which is aimed to provide a publication forum for important research in all aspects of mathematical biology and neuroscience. This journal will accept high quality articles containing original research results and survey articles of exceptional merit.
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Implementation of PID control strategies on Bergman model representing type 1 diabetes-T1D
In this work, we address Type 1 diabetes (T1D), a chronic autoimmune condition characterized by elevated glucose levels in patient’s bloodstream. We propose a robust approach for regulating blood glucose (BG) levels in individuals with T1D by utilizing a proportional-integral-derivative (PID) control method. The minimal Bergman model is utilized to represent the dynamics of glucose-insulin in the blood plasma. The proposed control strategy integrates the PID controller as a core element for BG regulation. Through simulations, our findings demonstrate the efficacy of the proposed controller in maintaining BG levels close to a target value of 80 mg/dL, starting from a state of hyperglycemia, even amidst various perturbations associated with meal intake.
Implicit numerical approach for biological Schnakenberg model employing finite element method (FEM)
Finite Element Method (FEM) based numerical techniques for two-dimensional and two-directional problems are challenging for numerical analysis practitioners. In this study, an implicit numerical scheme was developed to solve a set of coupled non-linear partial differential equations using the finite element method. This study presents a numerical approach using Finite Element Method (FEM) to implicitly solve the Schnakenberg biological model. This method uses the inherent advantages of the finite element method, such as its adaptability and ability to deal with complex geometries, while also introducing a strategy to improve stability. A system of algebraic equations is derived from the model equations to compute spatiotemporal dynamics by discretizing the spatial domain. The numerical solution is obtained by iteratively solving the resulting algebraic equations, by employing suitable linear solvers and convergence criteria. The results also demonstrate that this method captures intricate spatial patterns of morphogenesis concentration in animal species. Furthermore, the objective of this study is to analyze stripe and spot-like patterns during morphogenesis in animal species.
Optimal control of cardiovascular diseases among HIV infected
In this article, we formulated a new model of cardiovascular diseases as a complication of HIV infection and its HAART treatment with optimal control strategies. The stability of the equilibrium point for the model without control is established via the Routh Hurwitz criterion. In addition, our model is linked to three control measures, including the organization of programs to prevent HIV infection, awareness of the infected about the impact of HIV and HAART, and regular diagnosis and monitoring of risk factors of cardiovascular diseases in HIV-positive people. The objective function of optimal control problem aims to minimize the number of complications and associated costs. Then, we characterized the optimal controls by applying Pontryagin’s Maximum Principle after having proven its existence. We used Gauss Siedel’s iterative approaches to solve the resulting system. We used HIV data from Burundi to estimate fixed and adjusted parameters, to be able to provide numerical simulations to illustrate our theoretical results. Ultimately, the controls reduce the risk of cardiovascular diseases and improve public health.
Mathematical modelling of tumour chemotherapy by continuous infusion drug
We present a theoretical framework based on logistic growth and Michaelis-Menten kinetics for describing the interaction between tumour density and drug concentration, through an infusion pump. According to the logistics growth and Michaelis-Menten kinetics, the growth rate of tumours increases with the availability of drugs only up to a certain point. Cancer chemotherapy by continuous infusion pump has the advantage of achieving large concentrations of the drug at the tumour site while minimising adverse effects on the rest of the body, in contrast to conventional methods. The model in this work has aspects of logistic growth, which cover a method for determining tumour density and drug concentrations that will eliminate the tumour. Stability analysis is done by solving nonlinear equations and finding stable and unstable points, where the coordinates of the stable points represent the tumour density and the amount of drug. The stability of the equilibrium point for the model and illustrative numerical examples are provided to show the accuracy of the model.
Optimization of Moringa leaves (Moringa oleifera) diversification into antioxidant-rich Moringa-nori flakes as a food seasoning
This research focuses on optimizing antioxidant-rich Moringa flakes by fine-tuning blanching temperatures and nori content, which are key factors influencing the sensory qualities, antioxidant levels, and sodium content of the final product. Moringa leaves, recognized for their high nutritional value and antioxidant potential, were combined with different concentrations of nori to evaluate their impact on these characteristics. The study employed a factorial design with blanching temperatures of 70°C, 80°C, and 90°C, along with nori levels of 5%, 10%, and 15%, to identify the optimal conditions for creating a nutritionally superior and consumer-friendly food product. Statistical analysis was conducted using t-tests, two-way ANOVA, and Tukey post hoc tests to assess the significance of blanching temperature and nori content on antioxidant activity. The findings revealed that both factors significantly influenced the outcomes. Antioxidant activity was best preserved at a blanching temperature of 70°C, as higher temperatures caused degradation of heat-sensitive antioxidants. The optimal antioxidant activity was observed with a 10% nori content. The study concludes that carefully balancing blanching temperature and nori content is crucial for producing Moringa flakes that are rich in antioxidants. These findings offer valuable guidance for food product developers seeking to create health-oriented products with enhanced antioxidant properties, highlighting the importance of precise control over processing parameters. The successful creation of antioxidant-rich Moringa flakes underscores their potential in the health food market, offering a blend of nutritional benefits and consumer appeal.
Mathematical model of the social pathogen of HIV/AIDS stigma
This study incorporated HIV/AIDS stigma as a social pathogen to understand its impact on transmission and treatment. Integrating stigma into epidemiological models, we seek to quantify its effects on the spread of HIV, the progression to AIDS, and the success of treatment interventions. The results show that higher stigma leads to more infections, faster progression to AIDS and fewer treated individuals. The model highlights the need for stigma reduction interventions like education and supportive policies to improve health outcomes and control HIV/AIDS.
Stability analysis of cryptosporidiosis disease SIR model under stochastic perturbations
Using the known Cryptosporidiosis disease SIR model, a method of stability investigation for nonlinear systems of differential equations under stochastic perturbations is discussed. Stability conditions are obtained using the general method of Lyapunov functionals construction, the method of Linear Matrix Inequalities (LMIs) and MATLAB. The obtained results are illustrated via figures with numerical simulation of solutions of the system under consideration. The method can be applied for many other nonlinear systems of high order of nonlinearity in various applications.
A model of an optimal control for a discrete-time of brain drain
In this paper, we focus on the study of a mathematical model of the phenomenon of professional skills emigration in a region, by proposing a dynamic system model of non-linear differential equations in discrete time, considering four types of variables named: Permanents, Candidates, Emigrants, and Returnees. Our relevant objective is to find an optimal strategy to minimize the number of qualified individuals leaving their territory as well as candidates considering leaving their territory. The characterization of the optimal control analysis is based on Pontryagin’s maximum principle, aimed at characterizing an optimal control that minimizes the number of Emigrants and potential Candidates for emigration, in order to maximize the number of Returnees and Permanents. Numerical simulation was performed using MATLAB. Consequently, numerical illustrations of the obtained results are presented, confirming the effectiveness of the optimization strategy followed.
Statistical modeling of meteorological factors and PM2.5 levels: implications for climate change in Indonesia
Increased air pollution in Indonesia has resulted in fluctuations in climate patterns. The development of this research lies in the response variable studied, namely the concentration of PM2.5 which is the main indicator and a serious concern in Indonesia because the high concentration of these particles has a negative impact on public health. The Air Pollution Standard Index (ISPU) with the PM2.5 parameter is used to measure air quality based on the amount of PM2.5 levels in the air. ISPU with the PM2.5 parameter can show two possible levels of air quality, namely dangerous or not so that air quality data seen from the ISPU level of the PM2.5 parameter is binary. Meteorological factors that are thought to affect PM2.5 concentrations are air temperature, rainfall, solar irradiation, air humidity, air pressure, and wind speed. This study uses a binary logistic regression analysis method that aims to determine the influence of meteorological factors that are thought to affect PM2.5 concentrations so that they have the potential to affect climate change in Indonesia. The results of the analysis show that Indonesia with provinces that have PM2.5 concentrations still dominate, with a dangerous category of 52.94%. The meteorological factors that have a significant effect on PM2.5 concentrations are air temperature, rainfall, solar irradiation, air humidity, air pressure, and wind speed. In addition, climate change in Indonesia is also influenced by these factors. The research findings show that these characteristics have consequences for the Indonesian government's initiatives aimed at improving air quality and addressing climate change. Therefore, this is in line with the objectives of achieving the Sustainable Development Goals (SDGs), such as promoting Good Health and Wellbeing (SDG 3), creating Sustainable Cities and Communities (SDG 11), and undertaking Climate Action (SDG 13).
Performance convolutional neural network (CNN) and support vector machine (SVM) on tuberculosis disease classification based on X-ray image
Tuberculosis (TB) problem continues to be a significant health issue worldwide, with a specific emphasis on developing countries. Early diagnosis of TB can aid effective treatment and prevent disease transmission. Image-based X-ray classification of tuberculosis has become an interesting research topic in the development of automatic diagnostic systems that can assist doctors in making better decisions. In this research, the performance of the Convolutional Neural Network and Support Vector Machine in the X-ray image-based classification of tuberculosis was compared. The data used consisted of 1400 X-ray images from tuberculosis and normal patients, comprising 700 tuberculosis images and 700 non- tuberculosis images. The results showed that CNN outperformed SVM in the classification of tuberculosis based on X-ray of thorax. CNN achieved an accuracy of 97.86%, while SVM only reached 96.07%. Additionally, CNN also had higher recall and precision values than SVM, indicating that CNN is more suitable for use in X-ray image-based TB classification. In conclusion, this study demonstrated that CNN is superior to SVM in X-ray image-based TB classification. However, further research is needed to enhance the performance of CNN and SVM algorithms in X-ray image-based TB classification using more sophisticated techniques.
Topic modeling for user feedback dataset
In the era of big data, user feedback from mobile applications provides valuable insights for improving performance and user experience. However, extracting meaningful topics from large textual datasets remains a challenge. This study employs the Top2Vec model, a modern topic modeling technique, to analyze a dataset containing 15,000 user feedback entries from 15 different mobile applications across various categories. Unlike traditional methods like Latent Dirichlet Allocation (LDA), Top2Vec integrates word embeddings and clustering algorithms to identify topics based on semantic relationships. The research involves text preprocessing, embedding generation using Doc2Vec, and applying the Top2Vec algorithm to extract relevant topics. Results indicate that Top2Vec automatically determines topic numbers, offering richer and more interpretable topics compared to LDA and Embedded Topic Model (ETM). Evaluation metrics such as Coherence Score and Topic Diversity demonstrate that Top2Vec performs well, capturing significant patterns and addressing user concerns, including app glitches, performance issues, and user experience. This article highlights the effectiveness of Top2Vec in analyzing user feedback, making it a promising tool for understanding user needs and improving application development.
Transmission dynamics of yellow fever with toxic infected population
Yellow fever is currently affecting the African subcontinent, with Ghana accounting for the majority of confirmed cases (37.7%). As infections resurface in regions that have been free of yellow fever for more than a decade, it has become crucial to develop a mathematical model that accurately represents the transmission dynamics of yellow fever within a toxic infected population. The analysis of the existence and stability of the models’ equilibrium points is conducted. The sensitivity index study revealed that a, β1, β2, Λ, γ were the most sensitive parameters influencing the spread of yellow fever. The model is numerically solved using MATLAB ODE45 to determine its epidemiological implications. Preventing the advancement from infected (IH) to toxic infected (DH) individuals is essential, necessitating prompt intervention; hence, to mitigate the spread, it is imperative to decrease the contact rate between DH and the susceptible individuals. The dynamics of DH emphasize the significance of focusing on severe cases, for controlling outbreaks. Also, the stabilization phase of infected vectors suggests that measures aimed at vector reproduction or mortality may help limit the spread over time.
Hypertension modelling using nonparametric ordinal logistic regression based on multivariate adaptive regression spline
Hypertension is one of the most common diseases in the world and is an important risk factor for heart disease and a significant contributor to mortality and morbidity in both developed and developing countries. Systematic reviews have been conducted to assess the prevalence of hypertension and its risk factors. To model the hypertension status, in this study we developed an ordinal logistic regression model into a nonparametric regression model and called it a Nonparametric Ordinal Logistic Regression (NOLR) model. Therefore, this study aims to model hypertension status based on several influencing factors, and identify these factors that the most influential on hypertension status using the NOLR model approach, because we assume an ordinal scale response variable with q categories to have an asymmetric distribution, namely a multinomial distribution. Next, to estimate the NOLR model of Hypertension status, we use a Multivariate Adaptive Regression Spline (MARS) estimator, because it can accommodate interactions between risk factors expressed in basis functions, making it suitable for high-dimensional data cases. Furthermore, selection of the best model is based on minimum value of Generalized Cross-Validation (GCV). The results are that the best MARS model of hypertension status has BF = 16, MI = 3, and MO = 1 with GCV value of 0.0353874, and R2 value of 49.13508%. Also, there are three predictor variables, namely age, body mass index and total cholesterol that significantly affect the hypertension status. In addition, the obtained estimation of nonparametric ordinal logistic regression model using the MARS estimator is valid for predicting the hypertension status with an accuracy value of 69.25%, sensitivity value of 66.47% and specificity value of 84.06%.
Time series method for forecasting model for amount of ginger plant production
The ginger plant is a medicinal plant with great potential to be developed as an ingredient in traditional medicine and a raw material for drinks and food. From 2015 to 2021, almost all of the crops in this rhizome group experienced an increase in harvested area, but only ginger plants experienced a decrease in production. This is due to unpredictable weather changes, which can affect crop yields. Good production results can help farmers and industry in processing ginger crops. Therefore, accurate forecasting is needed to determine the quality of decision-making. This research uses primary data from ginger crop harvest from January 2015 to December 2019. Several trials have been carried out using time series forecasting methods: Double Exponential Smoothing (DES) and Triple Exponential Smoothing (TES). The aim is to find the accuracy of several time series methods in predicting the amount of ginger production so that farmers do not fail to carry out scientific forecasting. This research shows that the best forecasting method is to use the TES forecasting model with a Mean Absolute Percentage Error (MAPE) value of 38.10% compared to DES with a MAPE value of 42.49%. This shows that the TES method is better and more capable of forecasting the amount of ginger plant production.
Assessing the performance of K-means and DBSCAN clustering methods in tuberculosis mapping
Tuberculosis (TB) remains a significant public health challenge, particularly in densely populated and under-resourced areas such as West Java, Indonesia. This study aimed to map and analyze the spatial distribution of TB prevalence by clustering regions based on variables including sanitation quality, population density, and TB rates. Secondary data from official sources were utilized, and clustering methods such as K-means and DBSCAN were employed to group districts and cities into distinct clusters. The K-means method identified five clusters, while DBSCAN formed four clusters with some noise. Performance evaluation using the silhouette index indicated that K-means outperformed DBSCAN. The clustering results revealed that regions with poor sanitation and high TB prevalence require prioritized public health interventions. This analysis underscores the potential of clustering methods to enhance public health planning by identifying areas in critical need of targeted TB control strategies, optimizing resource allocation, and supporting evidence-based decision-making.
Emotion classification in social media posts related to telecommunication services using bidirectional LSTM
Social media has become a vital platform for sharing opinions, with 139 million users in Indonesia as of January 2024. Telecommunications companies can leverage feedback from platforms like Twitter and Instagram to understand customer sentiment and improve service quality. This study applies Bidirectional Long Short-Term Memory (BiLSTM) and FastText word embeddings to classify emotions in social media posts related to major Indonesian telecom providers, including Telkomsel, Indosat, XL, and Axis. Using Borderline Synthetic Minority Oversampling Technique (B-SMOTE) to address class imbalance, the model categorizes six basic emotions: happiness, sadness, fear, anger, disgust, and surprise. The optimal model, trained over 18 epochs, includes 64 BiLSTM units, 128 dense layer neurons, a 0.3 dropout rate, a batch size of 32, and a learning rate of 0.001. It achieved 93.51% accuracy and a 93.48% F1 score on unseen data, demonstrating strong performance in predicting customer emotions. This approach provides valuable insights for improving customer engagement and service in the telecommunications industry.
Marshall-Olkin alpha power transformed extended exponential distribution
This study presents the Marshall-Olkin Alpha Power Transformed Extended Exponential Distribution, a new statistical model that improves the flexibility of the standard exponential distribution using the Marshall-Olkin Alpha Power Transformed Extended-X family of distributions. MOAPTEEx distribution depends on the parameters θ, λ, and α. The lack of closed-form solutions and the requirement for numerical methods are highlighted as we examine the Maximum Likelihood Estimation (MLE) method for parameter estimation. The performance of many estimating strategies, such as maximum product spacing (MPS), least squares (LS), and MLE, across a range of sample sizes is assessed; this is done using a Monte Carlo simulation exercise. The results show that MLE is the most reliable method, particularly for larger samples, while MPS performs worse for smaller samples. Applications to actual datasets provide additional validation of the MOAPTEEx distribution, showing its efficacy in simulating fiber strength datasets where outer-performed the other competing models.
Characterization method for more than three dimensions based on dependence and correlation using hybrid multiple correspondence analysis
Characteristics of a district refer to specific attributes that describe its condition and quality. Identifying these characteristics provides more precise insights into districts that require more attention in specific situations. These characteristics are determined based on the interdependence of categories. Dependencies among multiple qualitative and quantitative variables can be analyzed using multiple correspondence analysis (MCA) hybrid with cosine correlation. MCA is particularly suited for analyzing contingency tables with more than two qualitative variables. This study aims to identify the characteristics of objects based on the categories of qualitative variables and the characteristics of objects based on quantitative variables. Several qualitative variables with many categories may result in less representative information, potentially failing to reach 80% cumulative variance in two dimensions. Therefore, the novelty of this study lies in identifying characteristics using Euclidean distance with a variance percentage of 100% in more than three dimensions and used two types of variables. The data used in this study are eight qualitative variables with 49 categories and three quantitative variables from the Supporting Area Survey of Bandung Regency in 2023. The analysis results indicate that the cumulative variance in two dimensions is only 16.9%. Consequently, calculations were performed using an Euclidean distance matrix with 43 dimensions to achieve 100% cumulative variance. The results of the analysis revealed that 28 district groups were identified.
Quasi likelihood on linear mixed effect of binary response in longitudinal data
Longitudinal data is derived from repeated measurements over time, and when analyzing such data using logistic regression models, it is essential to account for the correlations induced by these repeated observations. To address this, a random component is incorporated into the linear predictor, transforming the model into a generalized linear mixed model (GLMM). In this approach, the linear predictor is no longer purely systematic due to the inclusion of the random component. Estimation of parameters in a GLMM cannot rely on the conventional maximum likelihood estimation method, as it must account for the random component in the linear predictor. A viable alternative is the quasi-likelihood method, which provides a framework for estimating these parameters. Among various quasi-likelihood-based approaches, the generalized estimating equation (GEE) is commonly employed, as it explicitly incorporates the correlation structure in the data through a specified "working correlation" matrix. In particular, an autoregressive structure is often chosen for this matrix. The estimation procedure is then carried out iteratively through the Fisher Scoring method, with convergence achieved after several iterations. To assess the performance of this methodology, simulation studies are conducted, followed by its application to real-world data for empirical validation.
Analysis of stability and environmental decontamination strategy for a fractional-order Ebola model for bat population
Bats are known reservoirs of the Ebola virus, making the control of the disease within bat population crucial for preventing human outbreaks. This study presents a fractional-order Ebola model to describe the dynamics of Ebola virus disease (EVD) in bat population, incorporating memory effects to provide a more accurate representation of disease spread compared to traditional integer-order models. We analyze the model’s global properties, including stability and equilibrium points, and propose a time-dependent environmental decontamination control strategy aimed at minimizing the number of infectious bats while reducing associated costs. Using numerical simulations with specialized methods for fractional-order systems, we validate the theoretical results and demonstrate the effectiveness of the control strategy. The findings highlight that the proposed control significantly reduces the number of infectious bats, underscoring environmental decontamination as a viable measure for EVD control in bat population.
The performance of polynomial ordinal logistic regression analysis on hypertension risk modeling
Hypertension prevalence in Indonesia is on the rise. The risk of hypertension exhibits a non-linear relationship with predictors such as age, where the risk increases with age but declines in older individuals. This study aimed to analyze the factors influencing hypertension risk using polynomial ordinal logistic regression analysis. Cholesterol levels and mean arterial pressure were identified as significant linear predictors of hypertension risk. Additionally, age showed a significant polynomial effect, achieving a classification accuracy of 76.7%. The polynomial ordinal logistic regression model demonstrated improved classification accuracy compared to the linear model, increasing from 67.8% to 76.7%. These findings highlight the importance of incorporating non-linear relationships in predictive models to enhance the accuracy of hypertension risk assessment.
Comparative analysis of self-supervised pre-trained vision transformers and convolutional neural networks with CheXNet in classifying lung conditions
Classifying lung diseases from images has been a challenging task for Deep Learning (DL) methods. Self-Supervised Learning (SSL) in particular has been widely recognized to be effective for pre-training, especially new methods such as DINOV2 ViT/S-14 and ConvNeXt-V2. In this research, Transfer Learning (TL) was conducted on the two models by using the NIH CXR-14 dataset to perform 15-class classification. Additionally, SwAV ResNet-50, DINO ViT-S/16, and CheXNet were adopted as the baselines. Evaluation results showed that DINOV2 ViT-S/14 is superior to the other three models pre-trained on ImageNet with 0.743 macro-averaged AUC, but is inferior to CheXNet which was pre-trained using the same NIH CXR-14 dataset albeit without the ”No Finding” class. However, the CheXNet only obtained 0.773 AUC with 0.328 recall. Further analysis on feature separability showed that both CheXNet and DINOV2 ViT-S/14 were unable to extract meaningful features that differentiate the ”No Finding” class with the other 14 lung conditions, confirming the finding from a previous study that this dataset’s labels is noisy, rendering it unsuitable for downstream TL tasks. However, DINOV2 ViT-S/14 showed similar attention visualizations with CheXNet on some classes despite being pre-trained on natural images from ImageNet. Therefore, despite the unsatisfactory performance in this dataset, DINOV2 holds great potential in similar future studies, but it may require pre-training the models on medical image datasets.
Hunting cooperation among predators effects on the dynamics of food-web eco-epidemiological model with additional food to predators
In this paper, an eco-epidemiological model with fear and internal competition in the first and second prey populations have been proposed and studied, the susceptible predator is fed on preys using Holling type-II and Lotka-Volterra functional responses in the presence of additional food and hunting cooperation to the susceptible predator. Furthermore, it is assumed that the infected predator is receiving treatment. The existence, uniqueness and boundedness of the solution have been studied. The conditions of local and global stability have been identified. The goal of this study is to determine the fear, additional food, hunting cooperation and treatment effect on the stability of the proposed system, it has been demonstrated that they play a significant role in regulating the system's stability. Finally, our analytical conclusions were verified numerically by Mathematica.
Modeling and stability analysis of liquidity risk contagion in the banking system with time delay
The modeling of contagious spread is a well-established concept in the field of infectious diseases. However, its recent application to the banking system has opened up new avenues for analysis. The theory of delayed differential systems constitutes an essential mathematical tool for addressing this issue. In this study, we specifically focus on liquidity risk within the banking system and investigate the global stability with and without this delayed risk. We formulate a model to examine the potential impact of central bank interventions on the economy, utilizing simulated data from the largest European banks. The methodology emphasizes the importance of research results and specifies key variables or factors considered in the model. Study objectives focus on the modeling and analysis of the stability of liquidity risk contagion in the banking system, with a particular emphasis on the temporal dimension. The connection between modeling contagious spread in infectious diseases and its recent application in the banking system is well-established. To reach these conclusions, the study employed a rigorous methodology, integrating advanced mathematical models and in-depth statistical analysis. This methodological approach led to significant findings that shed new light on the dynamics of liquidity risk contagion in the financial context. The practical implications of these results are crucial for various stakeholders. Risk managers within financial institutions can utilize our findings to identify potential vulnerabilities and implement more effective risk management strategies. Policymakers and regulators can use our results to shape monetary and macroprudential policies aimed at stabilizing the financial system. The study’s global stability perspectives also provide a basis for improving crisis management practices, ensuring that institutions are better prepared to handle liquidity shocks. Additionally, integrating advanced modeling techniques encourages innovation in financial risk management, equipping institutions with enhanced predictive and responsive capabilities. By specifying key variables such as asset liquidity, interest rates, and other relevant factors, the model provides a solid foundation for a more comprehensive understanding of the underlying mechanisms of liquidity risk contagion in the banking system.
A modified exponentiated inverted Weibull distribution using Modi family
This paper proposes a new extension of the Exponentiated Inverted Weibull distribution using the Modi Family, called the Modi Exponentiated Inverted Weibull (MEIW) distribution that adds an extra shape parameter, allowing for a wider range of shapes for failure rates. Mathematical properties were developed, including hazard rate, survival function, reversed hazard rate, quantile function, moments, order statistics, and Renyi Entropy. Maximum Likelihood Estimation is employed for parameter estimation, with the performance of the estimators assessed through Monte Carlo simulation. The new distribution is fitted to the two real data sets and compared with some existing distributions such as Exponentiated Inverted Weibull (EIW), Inverse Weibull (IW), and Weibull (WE) distributions. The goodness-of-fit statistics and information criteria values demonstrated that the new distribution fits better the two real data sets than the other distributions.
A fractional order model for the dynamics of tuberculosis spread
In this paper, we establish a mathematical model for Tuberculosis (TB) spread in a human population. The proposed mathematical model is in the form of a nonlinear fractional order differential equation system which is an extension of the SEIR epidemic model. The model is constructed based on grouping the population into five compartments, namely the susceptible sub-population compartment, the exposed sub-population compartment, the infected sub-population compartment, the quarantine sub-population compartment, and the recovered subpopulation compartment. It was shown that the stability of the equilibrium points of the model depends on the basic reproduction number, and the addition of the quarantine sub-population compartment decreases the number of basic reproduction. A numerical simulation is given to demonstrate the validity of the results. The analysis reveals that the convergence to the equilibrium points becomes faster as the fractional order increases.
Sensitivity parameter for a discrete-time logistic melanoma cell growth under virotherapy
Melanoma is a rare type of skin cancer but the most serious compared to other types of skin cancer. The study of melanoma growth is interesting to analyze so that related parties can determine how quickly this cancer spreads and determine the proper and efficient treatment method. This paper uses the mathematical modeling of tumor growth to describe melanoma growth in the presence of virotherapy. The model shows the interaction between melanoma and uninfected tumor cells, completed by a Logistic law as a classical fraction for population growth to represent the natural melanoma growth function. Then, this model is discretized by the Non-Standard Finite Difference Method, then solved numerically, and completed by the 4th Runge Kutta method for validation. Moreover, this study gave a sensitivity analysis of several parameters to see how much melanoma growth changes over these parameters. Finally, it can be shown that the melanoma cell growth rate and virotherapy rate have the most significant effect on the number of melanoma cells.
Model-based clustering approach for clustering of heart disease patients based on risk factors
Cardiovascular disease causes the most non-communicable disease deaths or 17.9 million people each year. One of the efforts that can be made to reduce the threat of heart disease death is the grouping of heart disease patients based on their risk factors. The risk factors are age, blood pressure, cholesterol, and maximum heart rate. The data in this study is continuous data with mixed distribution and cluster uncertainty. This research suggests a model-based clustering approach based on finite mixture models. This approach assumes that the data is generated by a mixture of probability distributions, where each distribution represents different clusters with different parameters. Model-based clustering allows each individual to have a probability value to enter another cluster, making it suitable when there is cluster uncertainty and determining the number of clusters can be done automatically. Therefore, clustering is performed using model-based clustering to automatically determine the optimal number of clusters and identify cluster uncertainty. Parameters of the model are estimated using the Expectation Maximization (EM) algorithm. The best model selection is determined based on the Bayesian Information Criterion (BIC) values. The clustering results obtained the best model EEI with the optimal number of clusters as many as two Clusters.
A fractional mathematical examination on breast cancer progression for the healthcare system of Jordan
Breast cancer remains a significant public health challenge worldwide, with rising incidence rates in both developed and developing nations. This study presents a fractional mathematical model to examine the progression of breast cancer within the healthcare system of Jordan. The proposed model integrates fractional calculus to account for the non-linear dynamics and long-memory effects characteristic of biological systems. It employs a compartmental framework, categorizing women into six states: Susceptible, Preclinical, Clinical, Treatment, Remission, and Death. Transition rates between these states are derived from local epidemiological data to ensure relevance to Jordan’s healthcare context. The model is analyzed for stability, disease-free equilibrium (DFEP), and endemic equilibrium (EEP), using fractional differential equations to explore the dynamics of breast cancer progression. Numerical solutions are obtained using the Modified Fractional Euler Method (MFEM), showcasing the impact of various parameters on disease spread and treatment outcomes. Results emphasize the utility of fractional-order models in capturing the intricate interplay of biological and clinical factors influencing breast cancer dynamics. This study provides valuable insights for policymakers and healthcare professionals, facilitating the optimization of resource allocation and the development of targeted intervention strategies in Jordan.
Dynamics of a Leslie-Gower food chain model with fear, and anti-predator capability
The dynamics of food chains and ecosystems depend heavily on fear and anti-predator activity. grasping how prey-predator interactions affect not just individual species but also the larger community structure and ecosystem functioning requires a grasp of these fundamental ideas. Therefore, a novel food chain model made up of the Lotka-Volterra interaction and a modified Leslie-Gower model has been presented for investigation in the presence of fear and anti-predator notions. The model's local dynamics were examined. Requirements for persistence were identified. The global dynamics were examined using the Lyapunov function. Investigations of local bifurcations had been conducted. Lastly, to validate the results and comprehend the impact of fear and anti-predators, a numerical simulation was employed.
Modeling of stroke risk using synthetic minority oversampling technique in multivariate adaptive regression spline model
The health sector represents the third goal of Indonesia's Sustainable Development Goals (SDGs), which is focused on ensuring healthy lives and promoting well-being for individuals of all ages. Stroke is one of the leading causes of mortality globally and is classified as a non-communicable disease (NCD). Early detection and accurate risk prediction are essential to prevent stroke occurrences and reduce related mortality rates. This study evaluates the impact of the Minority Oversampling Technique (SMOTE) on Multivariate Adaptive Regression Splines (MARS) models in predicting stroke risk, particularly in addressing imbalanced datasets. The data used in this study was collected from Universitas Airlangga Hospital (RSUA) between June and August 2023. To assess the effectiveness of SMOTE, we compare the performance of MARS models with and without oversampling. The results show SMOTE- MARS achieves higher accuracy compared to MARS model (93.50% vs. 89.00%), sensitivity (97.70% vs. 94.50%), specificity (80.70% vs. 73.97%), and AUC (89.20% vs. 84.23%), These results underscore the importance of addressing class imbalance in stroke prediction datasets to achieve more accurate and reliable outcomes. Incorporating SMOTE into MARS models proves to be a highly effective approach for enhancing predictive performance, offering a valuable tool for early stroke risk detection and prevention strategies.
Urban area road scene segmentation using InternImage-adapter model
With the increasing development of autonomous driving, there is a need for an accurate deep learning model to detect and segment important objects such as other vehicles, traffic lights, road signs, road segments, pedestrians, and drivers accurately. Urban road scene segmentation presents the greatest challenge due to the presence of numerous obstacles, including pedestrians, roadside vegetation, buildings, and various other elements. The proposed model is a combination InternImage as the backbone and taking the Adapter of ViT-Adapter applied in the first block of the backbone model. The outputs of the output of InternImage last block and adapter output will be combined by element-wise addition then fed to segmentor. The model evaluated by public dataset Cityscapes with mIoU as the measuring metric. The result achieved is 81.93 mIoU on test data. The addition of adapter on the first block to InternImage does improve the performance of standalone InternImage.
Mathematical modeling and simulation of stress phenomena for medical students with optimal control
Stress is a pervasive issue among medical students, arising from demanding academic workloads, psychological pressures, and limited recovery opportunities. The consequences of unmanaged stress include adverse mental health outcomes, impaired academic performance, and increased burnout rates. This paper presents a novel mathematical model that encapsulates stress dynamics, workload impact, secondary symptoms, and resilience. The model introduces two control variables: u(t), modulating the influence of workload, and v(t), enhancing resilience. A system of nonlinear differential equations describes the interaction among these factors. The framework leverages optimal control strategies to minimize stress levels and improve resilience sustainably. Numerical simulations demonstrate the effectiveness of these strategies, highlighting the potential for precise interventions to mitigate stress. This work provides a foundation for evidence-based decision making in academic and psychological support systems, offering insights into the effective management of stress in demanding educational environment.
Stability and bifurcation analysis of a discrete fractional order predator-prey Leslie-Gower model with fear effect, Allee effect, and interspecies rivalry
This paper discusses the analysis of a discrete fractional-order Leslie-Gower model with fear effects, Allee effects, and interspecies competition. The discrete model is obtained by discretizing the continuous model using the piecewise constant approximation method. The model has four fixed points, namely trivial fixed point, prey extinction fixed point, predator extinction fixed point, and interior fixed point. The trivial fixed point always exists, while the existence of prey extinction, predator extinction, and interior fixed points are determined by certain conditions. The stability analysis shows that there are topological differences that depend on the parameter and the size of the integration step. Bifurcation analysis is performed using center manifold theory and bifurcation theorem. By choosing the integration step as the bifurcation parameter, it can be shown that the model experiences period-doubling bifurcation and Neimark-Sacker bifurcation. Numerical simulations are carried out at the end of this paper to confirm the analytical results.
Stability and bifurcation of prey-predator model with disease in prey incorporating anti-predator and hunting cooperation
This study's main goal is to determine how the prey population's cooperation and anti-predator behavior affect the prey-predator model's dynamic with disease in prey with the fear interaction. For this purpose, a mathematical model with Holling type II functional response was proposed and analyzed. The existence conditions of the equilibrium points with their stability analysis were analyzed to determine the qualitative behavior of the model. Numerical simulations are performed to support our analytical results. It is obtained that fear has a stabilizing role, whereas hunting cooperation has a destabilizing role in the system dynamics. Periodic oscillations were observed in the model through bifurcation.
The use of likelihood-based threshold in estimating nonparametric regression models through the adaptive Nadaraya-Watson estimator
This study develops a nonparametric regression model using the Likelihood-Based Threshold through the Adaptive Nadaraya-Watson Estimator to model rice productivity data in South Sulawesi in 2023. The issue of data variability can be addressed by simultaneously using bandwidth and threshold to improve estimation accuracy, compared to using only bandwidth. This problem is solved by integrating an adaptive threshold, which allows the estimator to adjust to the characteristics of the data. This method considers the distance between data points and the variation, enabling a more responsive estimation of changes in data patterns. This research aims to obtain the best nonparametric regression model to forecast rice productivity data. The best model is determined using the criterion of the minimum Mean Squared Error (MSE). The analysis results show that the optimal values are h=0.92 and δ=0.99, with the smallest MSE value of 0.075, it produces accurate predictions.
Data recovery methods in composite similarity-based data fusion: Application to physiological vital signs
The functionality of a statistical framework for unified multivariate vital signs data fusion is seen; its flexibility for switching between the two data spaces. This paper develops data recovery methods for data fusion built on composite similarity measures using three distinct variable specific weighting methods - mean, median, and Orthogonalized Gnanadesikan-Kettenring (OGK). Using spatial covariance parameters derived from empirical patient data, the method successfully exhibits the ability to accurately recover eight different vital signs from its fused counterpart. Performance evaluation using Root Mean Squared Recovery Error (RMSRE), Root Mean Absolute Recovery Error (RMARE), and Root Standardized Mean Absolute Fusion Error (RSMARE) demonstrated that all three weighting approaches achieved comparable and highly accurate results, with parameters converging within ±0.01 of 1.0. The recovered signals closely matched the original data patterns, preserving both long-term trends and short-term fluctuations. Notably, the method proved computationally efficient and robust across different weighting approaches, suggesting broad applicability in clinical settings. This approach offers a promising solution for dimensionality reduction in complex physiological datasets while maintaining clinical relevance, with potential applications in patient monitoring systems and physiological modelling.
Implementation of differential evolution algorithm for mars modeling optimization on Indonesia composite index data
Nonparametric regression is applied as an alternative to parametric regression if the data to be studied does not meet all the assumptions of parametric regression. This study aims to model using the Multivariate Adaptive Regression Splines model integrated with the Differential Evolution algorithm on the Indonesia Composite Index data. Indonesia Composite Index reflects the overall performance of stocks on the Indonesia Stock Exchange, which is influenced by various macro and microeconomic factors that lead to erratic patterns. Thus, the MARS method was chosen because of its ability to capture nonlinear relationships and interactions among the independent variables. At the same time, the Differential Evolution algorithm was implemented to optimize the selection of model parameters. The MARS model is found by combining Basis Function (BF), Maximum Interaction (MI), and Minimum Observation (MO), with concern to the minimum value of Generalized Cross-Validation (GCV). The study results using MARS-DE indicate that the optimal combination of models is BF = 35, MI = 1, and MO = 2 with a GCV value of 0.0068. In this study, 6 independent variables were used. The study results showed that the monthly exchange rate (USD-IDR), inflation, interest rates in Indonesia, the Dow Jones stock index, and the Shanghai Stock Exchange Composite index are independent variables that affect the Indonesia Composite Index (ICI). However, the Nikkei 225 stock index does not influence the Indonesia Composite Index. The resulting model is based on the smallest Mean Squared Error value of 0.0034.
The long short-term memory model as the neural networks approach in modeling water supply structural production
Almost all cities in Indonesia are moving to find alternatives for providing clean water as the population increases, so the demand for clean water volume is also increasing. Water wastage issues arise as water production continues to rise, highlighting the need for accurate predictions of future water production levels. Modeling clean water supply structural movements as an effort to predict water needs in a city in the future is important. This can be done by considering water usage data over time and factors that trigger clean water demand. This research proposes a long short term memory (LSTM) model that adopts a neuro informatics model as the neural networks approach for modeling water supply. The architecture of the LSTM used in this research employs one hidden layer with 32 neurons. The findings demonstrate that LSTM model can predict water production levels accurately with mean absolute percentage error (MAPE) less than 5% both for training and testing data set. These results categorize the LSTM model as a reliable forecasting tool for water production levels. Therefore, modeling using the LSTM method is a preferable choice for predicting water production aiding relevant parties in planning clean water resources tailored to the needs of population.
Analyzing the mathematical model of non-small cell lung cancer stages and their impact on hepatotoxicity during immunotherapy treatment
Bronchial cancer is considered the leading cause of cancer-related mortality worldwide, in comparison to survival rates of other cancer types. Lung cancer treatments aim to eliminate cancer cells, destroy them, or prevent cancer cell division, using approaches such as immunotherapy. Despite the relatively better effectiveness and tolerability of immunotherapy compared to other treatments, severe side effects related to liver dysfunction, known as hepatotoxicity, can occur in patients. In this study, we evaluated the response of patients with non-small cell lung cancer (NSCLC) to this treatment. These responses are modeled by a system of differential equations based on cancer stage changes, which we analyzed both analytically and numerically. The study methodology encompasses model construction, establishing the existence and uniqueness of the solution, identifying equilibrium points, analyzing stability of equilibrium points using Routh-Hurwitz Criteria, and numerical simulations. The conducted dynamic analysis resulted in determining an asymptotically stable equilibrium point without any prerequisite conditions. The results of the analysis are validated using numerical simulations. This study can serve as an early prediction of cancer progression within a hospital population undergoing immunotherapy. Its objective is to monitor the disease’s behavior over time and to visualize the potential impact of this treatment on the incidence of hepatotoxicity in these patients.
Stability analysis of the two-dimensional advection-diffusion equation for particle distribution by the Crank Nicolson-alternating direction implicit method
Particle distribution that occurs in waste stabilization ponds is a phenomenon that can be formulated using mathematics. The proposed model is a two-dimensional advection and diffusion model. We develop the model using differential equations that consider the x-axis and y-axis. We will solve the equation with the crank nicolson-alternating direction implicit finite difference method. the goal is to show the stability analysis of the method used to solve the proposed model. The results obtained show that the method used obtains unconditional stability.
Evaluation of order preserving triclustering for 3-dimensional gene expression data and functional interpretation using gene ontology in breast cancer patients
Breast cancer accounts for approximately 30% of cancer-related deaths among women globally. Recent advancements in data science have enabled in-depth analysis of various diseases, including breast cancer, through the field of bioinformatics. This study aims to analyze gene expression data from breast cancer patients using the OPTricluster method and to evaluate the biological interpretation of the results through Gene Ontology analysis. To reduce the complexity of breast cancer data, gene filtering techniques are applied. Triclustering, a bioinformatics approach, is particularly effective for processing three-dimensional gene expression data. One such method, Order-Preserving Triclustering (OPTricluster), classifies genes based on similar expression orders across patients over multiple time points. In this research, OPTricluster was employed across various scenarios, utilizing gene filtering simulations with δ parameters in comparison to the TD Score. The optimal scenario was identified with an interquartile range (IQR) < 0.75 and δ = 1.1. The OPTricluster analysis identified a total of 68 triclusters, consisting of 7 constant triclusters, 46 conserved triclusters, and 15 divergent triclusters. Functional analysis revealed that constant and divergent patterns were associated with protein transport within the Biological Process category. Conserved patterns were linked to apoptotic processes. Furthermore, the Cellular Component analysis highlighted cytosol involvement, while the Molecular Function category consistently identified protein binding across all patterns.
Machine learning based classification of rice leaf diseases: A comparative study
Rice is a staple food for most of the world’s population, making its sustainable production essential. However, undetected outbreaks of rice leaf diseases often result in reduced production due to crop failure. Accurate identification of rice leaf diseases is an important step in effective disease management. Machine learning (ML) algorithms can be an effective solution for early classification of rice leaf diseases based on available data. This study compares the performance of five ML algorithms, namely K-Nearest Neighbor (KNN), Support Vector Machine (SVM), Random Forest, Decision Tree, and Naive Bayes, in classifying rice leaf diseases. The evaluation uses metrics such as accuracy, precision, sensitivity, F1 score, and training and prediction time. In addition, the analysis also includes ROC-AUC values and statistical tests such as Friedman test and Nemenyi post hoc test to determine the best algorithm significantly. The results showed that Random Forest had the best performance among the five algorithms with a ROC-AUC of 0.92 and an accuracy of 0.94, however, it is noteworthy that this particular algorithm requires a longer duration for both training and prediction compared to its counterparts. Ultimately, this study serves to provide invaluable insights and guidance for the selection of the most optimal machine learning algorithm, thereby facilitating more efficient and sustainable practices in the classification of rice leaf diseases, which is crucial for the advancement of agricultural productivity and food security.
Stochastic dynamic behavior for the prey-predator problem with Holling-type II functional response
The purpose of our study is to examine the stochastic stability of one of the important problems associated with ecology, namely the problem of prey and predators. This study was based on the type II functional response. After constructing the stochastic mathematical system that describes the problem, we demonstrated the system’s biological acceptability by providing the necessary conditions for the solution to be positive as well as studying the stationary distribution. By doing so, we may have studied the stability of the system. The comparison approach is often employed to determine the prerequisites for the extinction or persistence of prey. Finally, to demonstrate the results’ accuracy and realism, we present a numerical analysis of the problem in question.
Modeling Nipah virus dynamics and designing optimal control strategies
This study introduces a mathematical model designed to shed light on how Nipah virus (NiV) spreads. The model emphasizes the application of control strategies to contain the virus, considering two primary transmission pathways: direct contact and transmission through animal hosts, especially bats and pigs. The goal is to deepen our understanding of how the virus spreads and to propose strategies that aim to reduce the number of infections and increase recoveries during the observation period, all while keeping the costs of these strategies low. The mathematical framework provided enables the combination of different control strategies to effectively manage the transmission dynamics of Nipah virus. By utilizing Pontryagin’s maximum principle, we identify effective measures to curb the disease’s spread. Theoretical findings are then validated through numerical simulations performed using MATLAB.
Adaptive risk affinity in mammalian evolution via integer partition and factorization models
Many animal species, including humans, display risk-taking behaviors that are evolutionarily beneficial for survival, such as learning about predators or exploring high-stakes environments. However, the underlying evolutionary mechanisms driving this behavior, especially its link to reproductive dynamics, are not well understood. In this paper, we introduce a novel population dynamics model using Diophantine equations to reconstruct evolutionary pathways. Our approach leverages integer partition and factorization techniques to model discrete population changes in species exhibiting risk-taking and risk-averse behaviors. Unlike traditional continuous models, our framework allows multiple solutions, reflecting the diversity of evolutionary strategies. This model also demonstrates how environmental pressures shape adaptive risk affinity, influencing reproductive rates and survival. The implications for understanding species adaptively, particularly in mammals, are profound, offering new insights into evolutionary behavior beyond the constraints of classical game-theoretic approaches.
Fine-tuning VGG16 model for driver behavior classification
This study aims to improve the performance of the VGG16 model with fine tuning. The transfer learning method is adopted to accelerate the learning process. The fine tuning carried out includes adding layers to the VGG16 model, freezing the initial layer during the training process, and using an adaptive learning rate and using dropout. The VGG16 model with fine-tuning is used for multi-class classification of five categories of driver behavior. The learning results show an increase in accuracy of up to 99.54%, with a decrease in the validation loss value to 0.0278, compared to the VGGNet baseline without fine-tuning which only achieved an accuracy of 96%. Layer freezing also reduces the number of trainable parameters by more than 50%. Fine-tuning has proven effective in improving model performance by adjusting parameters in the final layer so that the model is able to capture specific features of the target dataset and maintain basic features with the initial freeze layer. Testing using a confusion matrix shows a high level of prediction accuracy. This study underlines the importance of applying fine-tuning to CNN models to improve driver behavior detection capabilities.
Stochastic dynamics of a targeted chemotherapy-cancer model
This study aims to provide a stochastic mathematical model of the growth of cancerous tumors with targeted chemotherapy, where the cells were divided into three types of normal cells, cancer cells and responsive cells. The stability and long-terms behavior of the given system was studied. It has been shown, under certain conditions, that the tumor-free equilibrium state is almost globally stable. Accordingly, we conclude that the prescribed therapy can terminate cancer cells and thus the value of the tumor growth rate is obtained. What was also concluded during the study is that if the tumor is small, targeted chemotherapy drugs can be used in a smaller amount to eliminate the tumor from the body with less damage to other healthy cells. And vice versa. Finally, in order to verify our results, we conducted a numerical simulation.
Systematic literature review of oil palm on sandy soils
Sandy soils are marginal soils that have potential in the form of land availability and limiting factors that pose challenges to oil palm cultivation. We believe mapping and improving these limiting factors can increase the potential of sandy soils to support oil palm cultivation. This systematic review aims to summarise and collect data on the results of oil palm research on sandy soils to obtain information on the growth, yield and nutrition of oil palm plants grown on various sandy soils. Only 24 articles were screened according to this systematic literature review's inclusion and exclusion criteria. Most of the studies were conducted in Indonesia and then Malaysia, with the soil types being the object of research: Spodosols, Latosols, Entisols, and Regosols. It is hoped that the summary of results and evidence from the 24 articles found can be widely accepted and adopted to improve knowledge and find research gaps in oil palm crop management in sandy soils.
Role of refuge in the dynamic of two prey - one predator food web model with fear and nonlinear harvesting
This paper proposes and studies a food web model consisting of three species: two prey and one predator. The model takes into consideration the impact of fear, refuge for the first prey, which is dependent on the predator, and nonlinear harvesting of each prey. Further, the predator consumes the prey according to a Holling-type interaction. The model's boundedness is investigated. The conditions for all points of equilibrium that are biologically possible and local stability have been studied. The global stability of the model was examined using suitable Lyapunove functions. At last, the model is solved using numerical simulation for a variety of parameter values, and the results are shown graphically to confirm the analytical results.
Truncated spline regression for binary response: a comparative study of nonparametric and semiparametric approaches
Type 2 diabetes mellitus is a chronic metabolic disorder with a growing global prevalence, especially in developing countries. According to the International Diabetes Federation, Indonesia ranks fifth in the world for the highest number of diabetes cases, with 19.5 million adults affected by 2021. Early detection and intervention strategies are critical in managing this disease, and predictive models play a vital role in identifying individuals at high risk. Recent advances in regression analysis have introduced nonparametric and semiparametric regression methods, particularly truncated spline-based regression, which offer greater flexibility in capturing complex relationships in data. This study compares the performance of nonparametric and semiparametric truncated spline regression models in classifying binary response variables, specifically in predicting type 2 diabetes mellitus status. The models were evaluated using deviance values and classification accuracy metrics, including sensitivity, specificity, and precision. The results showed that the semiparametric truncated spline regression model outperformed the nonparametric approach, with lower deviance values (42.46 vs 52.94) and higher classification accuracy (86.67% vs 76.67%). In addition, the semiparametric model showed better sensitivity (97.44% vs 92.31%), specificity (66.67% vs 47.62%), and precision (84.44% vs 76.60%), indicating a greater ability to correctly classify diabetic and non-diabetic individuals.
Modeling the effect of climatic factors on malaria incidences using an auto-regressive generalized linear model with lagged covariates
Malaria remains a significant public health challenge globally, with its transmission intricately associated with climatic factors. Understanding the time lag effect of these variables on malaria incidence is crucial for developing effective control strategies. The research used monthly malaria incidence data obtained from the Uganda Ministry of Health, along with climate data from the Uganda National Meteorological Authority to investigate the impact of climatic factors, specifically rainfall, temperature, humidity and wind, on malaria incidence in Arua District, using monthly data from 2020 to 2024. To capture both immediate and delayed effects, the study employed an autoregressive generalized linear model (AR-GLM) with lagged covariates. The results indicate that increased rainfall and humidity with specific delays are positively associated with the incidence of malaria, while changes in temperature show a complex and unstable relationship. In addition, the AR-GLM model, which incorporates these time-dependent effects, outperforms a standard GLM, as evidenced by lower Akaike Information Criterion (AIC) and Mean Absolute Percentage Error (MAPE) values. Residual analysis confirms that AR-GLM adequately captures the temporal dependencies in the malaria data, showing no significant autocorrelation in residuals. The findings contribute to the development of effective malaria control and prevention strategies tailored to the specific temporal dynamics of the climate-malaria interactions in Arua district, ultimately aiming to improve public health outcomes.
A new estimator of the gamma regression model: theory, simulation, and application to body fat data
The gamma regression model, a specialized generalized linear model, effectively analyzes continuous, positive, and potentially skewed dependent variables when standard linear regression assumptions are violated. However, this model remains susceptible to the multicollinearity problem. Therefore, in this paper we propose a novel two-parameter shrinkage estimator (GDK) to address this problem, theoretically establishing its relationship with existing estimators through formal theorems. Through comprehensive Monte Carlo simulations examining various collinearity scenarios and a real-world numerical application, we demonstrate the GDK estimator's superior performance via mean squared error comparisons. Both simulation results and empirical evidence confirm that our proposed estimator outperforms existing alternatives, offering improved reliability for gamma regression analyses when multicollinearity is present.
Transferring control strategies in epidemiological models using τ-equivalences
Mathematical modeling plays a crucial role in understanding and controlling infectious diseases. Traditional SIR models, including both demographic (incorporating births and deaths) and non-demographic variations, have been extensively used to develop control strategies. However, the transfer of control strategies derived from simpler non-demographic models to more realistic demographic models remains challenging. This research addresses this gap by exploring the concept of τ-equivalence, aiming to transfer control strategies derived from non-demographic SIR models to demographic ones. Employing numerical simulations and parameter optimization, we demonstrated that appropriately calibrated non-demographic models closely mirrored demographic model dynamics, particularly under moderate control intensities. Nevertheless, our approach faced limitations under scenarios requiring rapid and significant infection reduction, revealing potential stability challenges. Our findings highlight the practical value of the τ-equivalence calibration method, while acknowledging that its broader applicability across diverse epidemiological models warrants further investigation.
Analysis of the stability of a mathematical model for measles
The worldwide measles crisis has escalated into a significant public health issue due to its lethal nature, generating widespread anxiety. Our study presents a dynamic mathematical model constructed using comprehensive mortality data from the World Health Organization and actual data on measles outbreak propagation. By utilizing the Routh-Hurwitz criteria and formulating Lyapunov functions, we demonstrated both local and global stability for scenarios with and without the presence of the disease. Furthermore, we conducted a sensitivity analysis on the model’s parameters to assess their impact on the basic reproduction number, R0. Our theoretical results were substantiated through numerical simulations performed with MATLAB.
Optimal control model for the spatial spread of COVID-19: An interacting fluid flow approach
This study develops an optimal control model to analyze the spatial and temporal spread of COVID-19 using an interacting fluid flow approach. Susceptible and infected populations are treated as interacting inviscid fluids governed by Euler’s equations, allowing for the spatial dynamics of disease transmission to be captured effectively. Control interventions, specifically vaccination (targeting susceptibility) and medical treatment (enhancing recovery rates), are incorporated as key strategies to mitigate the spread of infection. The model’s spatio-temporal dynamics are explored using high-order computational methods, namely the weighted essentially non-oscillatory (WENO) scheme for spatial discretization and the fourth-order Runge-Kutta method for time integration. Numerical simulations demonstrate the effectiveness of the proposed controls, emphasizing that a strategic combination of vaccination and treatment significantly reduces disease prevalence, especially in densely populated regions. This modeling framework offers valuable insights for policymakers, emphasizing efficient resource allocation and strategic intervention planning to manage COVID-19 or similar infectious diseases effectively.
Classification of nutritional status in toddlers using the support vector machine method
Malnutrition among under-fives remains a significant public health issue, especially in Gowa District, South Sulawesi, Indonesia. Accurate determination of the nutritional status of children under five is essential to support targeted health interventions. This study applies the Support Vector Machine (SVM) method to classify the nutritional status of children under five based on 2022 data, considering two categories: malnutrition and good nutrition. This method uses four types of kernels, Linear, Polynomial, Sigmoid, and Radial Basis Function (RBF), to identify non-linear patterns and handle imbalances between data classes. The results show that the RBF kernel performs best, with a classification accuracy of 98.27% and an APER value of 1.73%. This confirms the SVM's ability to handle complex data without assuming linearity, making it a superior approach to other traditional and nonparametric statistical methods. This SVM-based approach offers a significant contribution to the analysis of the nutritional status of individuals under five, not only to improve the accuracy of decision-making in the public health field but also as a basis for further development for the analysis of other health data in the future.
Transfer learning approach with EfficientNet to enhance food recognition systems for health monitoring
Food image classification is a challenging problem with significant potential benefits for real-world applications such as nutritional and energy estimation. Most prior research has proposed various Convolutional Neural Network (CNN) architectures to tackle this issue. However, given the large size and diverse nature of food image datasets, there remains considerable room for improvement, particularly in terms of accuracy and training speed. Typically, neural networks trained on small image classification datasets benefit from using pre-trained weights from large-scale image classification datasets like ImageNet. In this study, we explore the balance between using pre-trained networks as feature extractors and fine-tuning networks for food image classification. By leveraging transfer learning with EfficientNetV2B0, we achieve higher accuracy in food image classification. On the largest publicly available food image dataset, FOOD-101, our proposed method improves the previous best accuracy from 77.40% to 81.62%, while maintaining a prediction speed of 23 ms on a GPU.
Investigating the efficacy of insecticides in controlling the spread of tungro virus in rice plants: a mathematical modeling approach
The rise in population and robust economic expansion have led to a heightened need for food, energy, and water resources. In such circumstances, food security becomes an indispensable necessity for human survival. However, while striving to uphold food security, we frequently encounter the challenge of crop failure due to pest infestations, particularly green planthoppers. These infestations can lead to a reduction in both the quality and quantity of crop yields, and they also have the potential to disseminate the destructive tungro disease virus, further compromising crop health. Utilizing a mathematical modeling approach, a complex five-dimensional nonlinear system of differential equations is formulated to depict the intricate dynamics between rice plants and planthopper pests in the transmission of the tungro virus. This approach is adopted to investigate the effectiveness of control measures in curtailing the transmission of the tungro virus via planthopper pests. The model includes two control measures, which are the application of insecticides and the removal of infected plants, aimed at mitigating the virus’s transmission. We conducted stability analysis and derived the basic reproduction number formula (R0) to examine the qualitative behavior of the model. Furthermore, the stability of the interior equilibrium was analyzed using the Monte Carlo method, allowing for a robust evaluation of system dynamics under varying parameter uncertainties. As the basic reproduction number is influenced by the two aforementioned controls and endemic conditions emerge when this number exceeds one, we performed a sensitivity analysis to assess the impact of these control measures on reducing the R0 value and infected compartment. Subsequently, we conducted an optimal control investigation to assess the efficacy of implementing these two control measures by developing various scenarios. Our results indicate that implementing both insecticide application and the removal of infected plants together is considerably more effective than implementing these control measures separately.
Dynamics of a dengue model with incubation periods and vertical transmission in a heterogeneous environment
Dengue fever is one of the most common insect-borne infectious diseases in the world. In this paper, a dynamics model of dengue fever with incubation periods and vertical transmission in a heterogeneous environment is developed, taking into account the influence of incubation periods and vertical transmission on dengue virus transmission. Theoretically the existence of a global classical solution of the model is proved uniquely, and the threshold dynamics of the model is described using the basic reproduction number R0. The global asymptotic stability of the disease-free equilibrium is proved by constructing the upper and lower solutions in combination with the properties of the basic reproduction number when R0 < 1, and the disease-free equilibrium is unstable when R0 > 1. There exists a global exponential attraction set in the system when R0 > 1. Finally, numerical simulation and PRCC sensitivity analysis were combined to obtain that increasing the diffusion coefficients of both susceptible and infected populations exacerbates the spread of dengue virus. In reality, dengue virus transmission can be effectively controlled by reducing the frequency of crowd activities, good personal protection against mosquito bites, timely medical treatment, and effective vaccination, among which the reduction of mosquito bite rate has the most significant effect.
Determining relative humidity in Surakarta city using semiparametric regression based on Fourier series penalized least square
This study discusses the use of a semiparametric regression model approach based on Fourier series penalized least square estimator to determine the relationship between relative humidity and dew point in Surakarta city of Indonesia. The proposed method can address complex climate data patterns. A dataset of 100 observations was analyzed under three training data scenarios, for sample sizes of 𝑛 = 70, 𝑛 = 80, and 𝑛 = 90. It yields the optimal Fourier coefficients of 2, 2, and 2, and smoothing parameter values of 0.018, 0.0124, and 0.039, with minimum generalized cross validation values of 4.410572, 4.191036, and 5.989094. The results of this study show that the proposed method provided good performance for prediction purpose with Mean Absolute Percentage Error (MAPE) values of 2.471245, 2.270436, and 2.93358. This means that category of the proposed method is highly accurate for prediction purpose. These results underline the ability of the proposed method to capture the inverse relationship between humidity and dew point. In other words, based on these results, this study highlights the effectiveness of the semiparametric regression model approach based on Fourier series penalized least square estimator in dynamic scenarios and recommends its application to other climate variables or regions to further evaluate its adaptability and resilience.
Small area estimation for morbidity rate prediction
Complete and up-to-date data is important for development. However, its provision is costly. Survey is more efficient data collection solution, but the available sample is sometimes unable to produce direct estimate with sufficient precision. Small area estimation is one of the solutions by increasing the effectiveness of the sample. Indicators need to be presented with good precision so that policies are right on target. One of them is the health indicator which is expressed by morbidity rate. Morbidity rate is the percentage of population with health complaints that interfere with activities. Precision morbidity data is needed as criterion for determining non-communicable disease prevention at regional level as mandated by Law No. 17 of 2023. However, direct estimation from the survey shows that there are still districts/cities with Relative Standard Error (RSE) more than 25% like in Papua Island. Even though, especially Papua Province has an increasing morbidity rate. For this reason, in this study, indirect estimation of SAE Hierarchical Bayes (HB) Beta-Logistic was carried out to obtain estimate with good precision (RSE less than 25%). The results emphasize that SAE HB Beta-Logistic provide the estimate of morbidity rate precisely than the direct estimates for all districts/cities on the Papua Island.
Optimizing tuberculosis dynamics through a comparative evaluation of mathematical models
Tuberculosis (TB) remains a major public health challenge, requiring precise mathematical modeling to enhance understanding and inform control strategies. Analyzing the dynamics of TB involves studying key model parameters to improve accuracy. This study evaluates six TB models using statistical criteria, including the Sum of Squared Errors (SSE), Akaike Information Criterion (AIC), corrected AIC (AICc), Bayesian Information Criterion (BIC), the difference in AIC (∆AIC), and Akaike weight. The results show that proposed model 2 outperforms the others, achieving the lowest AIC, AICc, and BIC values while having the highest Akaike weight. These findings underscore the importance of selecting an optimal model for TB dynamics to ensure reliable predictions and effective policymaking.
Graph-theoretical approaches to entropy in Cu₂O crystalline structures: implications for biomedical and energy applications
In molecular science, understanding the intricate connections between molecular structures and their biomedical and pharmacological properties has been a focal point of research, aided by experimental and computational approaches. A key tool in this exploration is the use of Topological Indices, which are numerical descriptors that reveal fundamental characteristics of molecular frameworks. These indices are particularly crucial in predicting the biological activity of new chemical compounds and pharmaceuticals by quantifying weighted entropies. In this study, we examine the concept of graph entropy in relation to the topological properties of the copper oxide crystalline structure (𝐶𝑢₂𝑂[𝑖,𝑗,𝑡]). Our goal is to unravel the mathematical complexity of 𝐶𝑢₂𝑂[𝑖,𝑗,𝑡] by integrating entropy with various topological indices, including weighted measures. We also present a graphical comparison that illustrates the interplay between these computed indices and their corresponding entropies, offering new insights into the structural and mathematical elegance of 𝐶𝑢₂𝑂[𝑖,𝑗,𝑡]. This analysis broadens our understanding of the material’s potential applications across fields such as chemical sensors, solar cells, photocatalysis, and energy storage, where the unique crystallography of 𝐶𝑢₂𝑂 plays a pivotal role.
Improving statistical process control for water quality in catfish farming with robust EWMA and alternative estimators
Water pH plays a crucial role in catfish (Clarias sp.) aquaculture, as pH imbalance can disrupt dissolved oxygen levels, weaken the fish’s immune system, and affect overall growth. Continuous monitoring is essential to maintain optimal water quality. The Exponentially Weighted Moving Average (EWMA) control chart is commonly used for pH monitoring, but its performance deteriorates when data exhibit non-normality. We propose a robust EWMA control chart incorporating interquartile range (IQR) and Biweight estimators to address this limitation and enhance sensitivity in non-normal environments. This study analyses pH data from catfish nursery tanks at the Bina Bersama Fishery Group in Makassar, Indonesia, collected from May 28, 2024, to June 27, 2024, across 10 samples. We evaluate the control charts using different smoothing parameters (λ = 0.01, 0.5, and 1) and assess their performance based on Average Run Length (ARL). The results indicate that the Robust EWMA control chart with the IQR estimator outperforms the Biweight estimator, achieving an ARL of 1 at a more minor process shift (0.2) compared to 0.5 for Biweight. The optimal configurations are obtained at λ = 0.01, with μ0 = 7.8287 and σ = 0.039 for IQR, and σ = 0.055 for Biweight. These findings suggest that the IQR-based Robust EWMA control chart is more effective in detecting small shifts in pH, providing a superior monitoring tool for ensuring stable water quality in catfish aquaculture.
Expanded spatial Durbin model for analyzing stunting prevalence in Java Island
Stunting is a chronic health problem that impacts children's physical and cognitive development, especially in developing countries like Indonesia. There are several exogenous factors that influence the prevalence rate of stunting. Therefore, when examining spatial aspects, there is a possibility that the spatial dependences are occured not only on the response variable but also on the exogenous variables. Thus, a model is required to consider these spatial dependences. The Expanded Spatial Durbin Model (ESDM) can be used to predict stunting prevalence influenced by exogenous variables. We used the Euclidean method to determine the inverse distance weight matrix, and the Moran Index test was applied to identify autocorrelation. By incorporating spatial effects and relevant exogenous variables, the model can provide more precise estimates of stunting prevalence in different regions. This modelling technique is very effective for increasing the accuracy of stunting prediction, considering exogenous factors such as malnutrition prevalence and human development index (HDI) where all variables contain spatial dependencies. For the study, we choose Java Island in Indonesia as one of regions with a highest population density and significant stunting rates. Using the proposed technique, we found that the malnutrition variable has much stronger effect on the stunting prevalance than the HDI variable.
Hunting cooperation among predators effects on the persistence and bifurcation of food-web eco-epidemiological model with additional food to predators
In this paper, the local bifurcation's occurrence conditions have been established for a food web eco-epidemiological model of four species, including first prey, second prey, susceptible predator, and infected predator with fear effect, and internal competition among prey populations, incorporating additional food resources and hunting cooperation among predators, and disease dynamics with treatment in the predator population with Holling type-II and Lotka-Volterra functional response. This model has fifteen equilibria, the saddle-node bifurcation have been shown close to the interior equilibrium points 𝑃13 and 𝑃14, also at the first-second prey-free equilibrium point 𝑃7, and the second prey-free equilibrium points 𝑃9 and 𝑃10 a transcritical bifurcation occurred, while at the preys-infected predator-free equilibrium point 𝑃3, the predators-free equilibrium point 𝑃4, the second prey-infected predator-free equilibrium point 𝑃5, the first prey-infected predator-free equilibrium point 𝑃6, the infected predatorfree equilibrium point 𝑃8, first prey-free equilibrium points 𝑃11 and 𝑃12 have a transcritical and pitchfork bifurcations. Furthermore, conditions for Hopf bifurcation close to positive points 𝑃13 and 𝑃14 have also been examined. Numerical results for the set of hypothetical parameters support our analytical results regarding the persistence of this model and the occurrence of bifurcation using Mathematica.
Reversible (bisymmetric) self-dual codes over finite fields with characteristic two and their applications to DNA codes
Some recent studies reveal the development of reversible (bisymmetric) self-dual codes over fields of order 2 and 4. In this paper, we give new methods of constructing reversible (bisymmetric) self-dual codes over finite fields with characteristic two. This approach is motivated by the well-known reversible (bisymmetric) self-dual codes over finite fields of order two. We first investigated some properties of a reversible (bisymmetric) self-dual code over finite fields with characteristic two. Next, we developed a method to construct a new reversible (bisymmetric) self-dual code over finite fields with characteristic two. Additionally, we found an optimal reversible (bisymmetric) self-dual code over finite fields with characteristic two, and this method is applied to construct DNA codes.
Menu planning using multi-complex differential evolution algorithm for wasting children
Despite Indonesia's stable economic growth, child wasting remains high, particularly in Nusa Tenggara Timur (NTT) Province, reflecting a disparity between economic progress and public health. The complexity of this issue is exacerbated by the low level of women's education in NTT, while climatic factors and soil conditions further impact food availability. We used the Multi-Complex Differential Evolution algorithm to serve as an effective and efficient tool for mothers in planning a diverse selection of nutritious meals for their children based on food availability and parental economic capacity. The algorithm analyses local food resources and suggests meal plans that maximise nutritional value within available ingredients. Optimising food combinations ensures children receive balanced nutrition, addressing deficiencies contributing to child wasting. The findings indicate that this algorithm performs well with a population size of 30 and a maximum of 1,000 iterations using the DE/rand/1 mutation function. Moreover, with these parameters, the algorithm generates various healthy meal plans that meet multiple constraints while ensuring a short execution time.
Computational analysis of molecular descriptors for anti-tuberculosis drugs used in tuberculosis treatment through quantitative structure-property relationships
Tuberculosis poses a major public health challenge due to its widespread prevalence and severe health impact, necessitating the development of effective therapeutic agents. This study analyzes the structural and physicochemical characteristics of 13 anti-tuberculosis drugs, including Isoniazid, Levofloxacin, and Bedaquiline, using distance-based topological descriptors, particularly the Mostar index. A computational approach involving the Mostar index and Quantitative Structure-Property Relationship (QSPR) analysis was employed to predict critical drug properties like melting point and molar mass. The findings revealed strong correlations (melting point R > 0.990, molar mass R > 0.970), demonstrating the predictive potential of the Edge Mostar index. These results offer valuable insights into the structural properties of anti-tuberculosis drugs, supporting the development of novel agents by leveraging the Mostar index for improved drug design.
Dependency-based clustering using correspondence and Ward's hierarchical analysis: a case study on clean water and sanitation indicators in West Java's cities and regencies
Correspondence analysis is a graphical technique for depicting relationships between variables in a low-dimensional space, making it ideal for non-metric data and non-linear associations. Multiple Correspondence Analysis (MCA) expands on this by identifying patterns in categorical variables, using the Burt matrix, a multidimensional contingency table. MCA aims for a cumulative variance of at least 70% across two dimensions; however, if this threshold is not met, Euclidean distance can improve object characterization with results extending beyond two dimensions. Though the dependency information from correspondence analysis is objective, it cannot reveal groups with fewer members based on available resources. Hence, cluster analysis is conducted using the principal coordinates from MCA results. This study aims to identify the unique characteristics of each object, allowing more focused evaluations based on specific attributes. By ensuring a cumulative variance of 100%, this method captures all relevant dependency information, offering a deeper understanding of variable relationships. The study stresses the importance of selecting the most suitable clustering model that aligns with the correspondence analysis results. By combining MCA and hierarchical clustering, the study visualizes and groups regencies and cities based on their clean water and sanitation conditions. Initial MCA results showed a cumulative variance of 22.3% in two dimensions, requiring further adjustments for more accurate interpretation. The innovation of this research lies in integrating MCA with hierarchical clustering using Euclidean distance to explore characteristics comprehensively. This method ensures a complete representation of dependency relationships, maintaining a cumulative variance of 100%. A Euclidean distance matrix across 63 dimensions was used to enhance objectivity. The results identify 18 groups of regencies and cities with similar clean water and sanitation characteristics. Among clustering methods, the Ward method was most consistent with MCA findings. Cluster analysis was performed by forming three, four, and five clusters, aligning with government budget constraints.
Modeling the impact of food insecurity on the transmission dynamics of monkeypox using three different fractional operators
The global emergence of Monkeypox presents significant public health challenges, particularly in regions with varying levels of food insecurity. This study develops and analyzes a novel mathematical model examining the dynamics of Monkeypox transmission across food-secure and food-insecure human populations, while incorporating animal reservoirs. We investigate the system through three distinct arbitrary-order derivative operators: the Caputo derivative with power law, the Caputo-Fabrizio derivative with non-singular kernel, and the Atangana-Baleanu derivative incorporating the Mittag-Leffler function. The model explicitly considers the impact of food insecurity status on disease transmission rates, recovery patterns, and intervention effectiveness. Through numerical simulations, we demonstrate that food-insecure populations experience significantly higher infection peaks (approximately 12.5 million cases) compared to food-secure populations (approximately 9.5 million cases). Our analysis reveals how varying fractional orders (θ = 0.95, 0.85, and 0.75) influence the temporal effects and overall disease dynamics. The model parameters, estimated from current epidemiological data and literature, provide insights into the critical role of food insecurity in disease mitigation. Surface plots analyzing the basic reproduction number R0 against various parameters demonstrate the sensitivity of disease spread to contact rates, recovery rates, and food insecurity status. These findings emphasize the importance of integrating food security measures into public health interventions for effective Monkeypox control, particularly in vulnerable populations.
Oncolytic virus therapy through mathematical modeling: the infection-lysis trade-off in cancer dynamics
One of the most fatal diseases globally is cancer. Its incidence continues to rise even though early detection methods and therapeutic approaches have been enhanced. So we necessitate ongoing research into its underlying causes and new treatment paradigms. In this paper, we study a mathematical model to treat cancer by oncolytic viruses (OVs), like adenovirus ONYX-15. The model incorporates three variables: the uninfected tumor cell density, the infected tumor cell density and the oxygen concentration. We prove that solutions exist, are non-negative and bounded, and we analyze equilibrium points along with their stability. We find that engineering an effective oncolytic virus requires a finely tuned interplay between two key properties: the virus’s ability to infect tumor cells, and its oncolytic potency. If the virus is excessively cytotoxic to tumor cells but insufficiently infectious, infected cells will be destroyed faster than spreading the infection. This imbalance reduces the overall therapeutic efficacy, as the virus fails to propagate adequately through the tumor population.
Asymptotic properties of molecular mechanism models with functional response
In this study, several modified types of the Goodwin model are proposed to demonstrate oscillatory behaviors. The original Goodwind model is the prototype model of a negative feedback loop that exhibits oscillations. But it exhibits oscillations when the cooperativity is very high, n > 8, which is unrealistic in most biological situations. We show two cases of a modified Goodwin model with functional responses of order n = 5 and n = 6 which exhibit periodic oscillations. It is shown that the modified functional responses lead to produce oscillatory solutions in these cases. This result suggests the possibility of constructing models to have oscillatory solutions with lower order functional responses than the requirement n > 8 for the original Goodwin model case.
Evaluation of specific activity and decay characteristics of radionuclides in cancer treatment
Radiation therapy is a treatment modality of cancer. This treatment technique always needs to be executed very carefully, by considering lots of Dosimetric properties and quantities. Internal beam radiation therapy which is also known as brachytherapy requires extra degree of such practices for being more complex. Radioactive elements are used as energy source so that they can deposit the required energy to unwanted tumor and ultimately kill the DNA of tumorous cells. In this work various properties of the radioactive elements have been evaluated. The analysis was extended to know the impact of such properties and quantities. The elements under consideration were radium-226, radon-222, Cobalt-60, and Cesium-137. The change in the specific activity which was caused by the radioactive decay found to decrease with time, but this decrease vary in different elements for having various basic physical properties.
Numerical simulations of inland fisheries mathematical models
This research focuses on numerical simulations of the prey-predator mathematical model in inland fisheries. The problem of excessive harvesting results in unsustainable harvesting so fishermen will spend capital for restocking the fish population. Mathematical models can provide ideal harvesting effort calculations to obtain a sustainable harvesting strategy to reduce the cost of harvesting in the following period. Two mathematical models were created in this paper. The first model considered a condition in which there was no interaction between prey and predator, and the second model considered a condition in which there was interaction between prey and predator. The first model assumed that a juvenile fish population (x1) was introduced and grew into native adult fish (x2) and the native adult fish reproduced spawn fish (x3). The second model behaves like the first but adds a predatory fish population, and assumes it interacts with the introduced juvenile stock fish population (x1) and the spawn fish population (x3). Dynamic analysis of the mathematical models is carried out to obtain the equilibrium points and their stability analysis. Numerical simulations of both models were done using the Euler method to show that the maximum sustainable yield effort (EMSY) value influences the number of fish populations in inland fisheries because harvesting effort will maintain sustainable harvesting. The simulation suggests that if the harvesting effort is above the 2EMSY value, the fish population will approach the equilibrium point (0,0,0) in the first model and (0,0,0,0) in the second model. However, if the harvesting effort is less than or the same as the 2EMSY value, the fish population will approach the equilibrium point when adult fish and spawn fish exist in both models. In conclusion, determining harvesting efforts following the EMSY value is expected to support sustainable harvesting so that the economy of inland fishery can be sustainable.
Socio-demographic and clinical factors in stroke patients: a survival analysis approach
Stroke is a serious medical condition that occurs when blood flow to a part of the brain is either disrupted or cut off. It is one of the leading causes of death worldwide and is classified into two main types: hemorrhagic (caused by bleeding) and ischemic (caused by blood vessel blockage). This study aims to identify the factors significantly influencing the rate of clinical improvement in stroke patients at RSKD DADI Hospital, Makassar, South Sulawesi Province. The analysis was conducted using the Extended Cox Regression model, with the dependent variable being the length of hospitalization until the patient was declared improved or discharged. The independent variables included gender, age, hypertension, cholesterol levels, diabetes mellitus, type of stroke, and uric acid levels. The results indicated that the type of stroke did not meet the proportional hazards assumption, suggesting that the effect of stroke type varies over time. Of the factors examined, patient age, cholesterol level, and type of stroke were found to significantly impact the rate of clinical improvement in stroke patients at RSKD DADI Hospital, South Sulawesi Province.
Predator control policy for prey-predator system with group defence in prey and Allee effect in predator
The present work discusses a simple two-species model of a predator-prey with group defense for prey species and a weak Allee effect. The local dynamics revealed that the system could undergo Hopf bifurcation as well as have an extinction domain. Combinations of different control methods have been thoroughly researched, and the policy reduces the predator population and increases the prey population simultaneously. Finally, some numerical illustrations are provided to validate our analytical results using various parameter sets. According to the findings, increasing the parameter value of γ (aggregation efficiency) under the optimal control strategy does not affect on predator or prey biomass.
A mathematical model of HIV/AIDS with awareness and its application to optimal control strategies: a case study in Thailand
HIV infection can progress to AIDS, the most severe stage of the disease, characterized by a critically weakened immune system. In some regions, AIDS is a leading cause of mortality. This study develops a mathematical model of HIV/AIDS aimed at reducing new infections, using Thailand as a case study. The model includes epidemic and endemic analyses, along with stability evaluations for both equilibrium points. Additionally, an optimal control analysis is conducted to identify strategic interventions for minimizing all stages of HIV infection.
Bayesian reasoning and SIR malaria models
Various sources of uncertainty are involved in malaria modelling, arising from intricate interplay between parasite biology, vector ecology, human factors and environmental variables. These uncertainties are magnified by data constraints, the spread of drug and insecticide resistance and the difficulties associated with reliably accounting for intervention effects and long-term climate impacts. It is imperative to employ complicated statistical techniques, ensemble modelling approaches and consistently improve models as new information becomes available for purposes of offering strong guidance to public health decision-making about the inherent complexity and fluctuation in transmission dynamics of malaria. To assess the impact of intervention measures put in place, it is important to quantify the uncertainty and take it into account when making decisions. Bayesian inference makes this possible in the sense that the posterior parameter inference can characterize uncertainty in the estimates of unknown parameter values and indeed the uncertainty over a set of candidate models. In this work, we apply Bayesian inference based on Markov chain Monte Carlo (MCMC) sampling to a compartmental models (SIR) Ross’ original model. We define a ground truth, subject it to actual data and infer the posterior distribution of the initial state and the parameters of the model. We investigate several scenarios for the observations generated corresponding to realistic situations. This way, we can contrast the inferred posterior to the ground truth and the amount of uncertainty injected in the observations.
Binary logistic regression with random effects for productivity analysis in mining operations
Binary logistic regression is a statistical method used to examine the relationship between a binary response variable and predictor variables, measured on a categorical or continuous scale. Binary logistic regression modeling is typically applied to cross-sectional data; however, this study extends its application to a binary logistic regression model for longitudinal data, which combines cross-sectional and time-series data. In longitudinal data, time and individual variables are critical components associated with random effects, as fixed predictor variables often do not fully explain temporal variations and inter-individual differences. Furthermore, the response variable is influenced by predictor variables (fixed effects) and random factors (random effects) such as sample selection, time, and area. A model that incorporates fixed and random effects components is called a mixed-effects model. This study develops a mixed-effects logistic regression model by considering the longitudinal data structure and predictor variables as random effects. The analysis is applied to loading equipment productivity data at PT Kaltim Prima Coal, with variables such as spotting time and loading time as fixed effects and environmental factors beyond control as random effects. This approach improves parameter estimation accuracy to 74.63% and provides a deeper interpretation of the factors affecting productivity.
Mathematical modelling of co-infection of Lassa fever and COVID-19
The prevalence of Lassa fever (LF) and COVID-19 co-infections has been increasing, primarily because their modes of transmission are closely related, making individuals highly susceptible to co-infections. While there is no vaccine for LF, COVID-19 has one. Due to their significant implications, this situation necessitates implementing effective control measures to prevent a co-epidemic of these two diseases in our society. To address this, a deterministic model for LF and the COVID-19 epidemic is considered, highlighting consequences that should be addressed to avoid the challenges associated with a co-epidemic. The model undergoes qualitative analysis, and the primary reproduction number (R0) is derived. Criteria for the stability of each model equilibrium are established. The model is numerically solved and simulated for different co-epidemic scenarios, and the findings from these simulations are discussed.
Enhancing water level forecasting in the Ciliwung river using multiple input BiLSTM
Accurate forecasting of river water levels is crucial for flood disaster mitigation, especially in flood-prone areas such as Jakarta, Indonesia. We propose a deep learning model for water level forecasting using a Multiple Input Bidirectional Long Short-Term Memory (MI-BiLSTM) architecture enhanced by an outlier-handling framework based on DeepAnT and linear interpolation techniques. Water level data were collected hourly from three monitoring stations: Katulampa Barrage, Depok Gauge, and Manggarai Gate. Two prediction scenarios were evaluated: the model with raw data and DeepAnt-BiLSTM model based on integrated process. The proposed model showed a significant improvement in the predictive performance, achieving an RMSE of 10.81 cm, MAPE of 1.07%, and NSE of 0.94. In addition, when evaluated based on the flood alert classification, the model accurately detected 130 out of 155 alert-level events (water level > 750 cm) in the testing set, achieving an alert classification accuracy of 83.87%. These results demonstrate the capability of the model to capture extreme hydrological events and its practical suitability for early warning systems. This study highlights the potential of combining outlier handling and BiLSTM-based architectures to enhance the accuracy of water level forecasting. The proposed approach is particularly relevant to improve the performance of prediction models and supporting the development of a more reliable flood early warning system.
Effect of wind and disease on the dynamical behavior of a prey-predator system
Considering the significance of prey-predator models in the environment, these models illustrate the relationship between living things and their interactions. In this paper, a prey-predator model was advanced and studied that included the wind flow and disease in prey. This study aims to understand how these factors affect the behavior of species. The solution properties of the proposed model were examined. Also, all potential equilibrium points and their stability were studied. In addition, the persistence conditions that ensure the continued existence of organisms were calculated. The theoretical results were supported by numerical analysis by using the MATLAB program (version R2018b), which also explained how changing parameter values ​​affected the dynamic behavior of the prey-predator model. Our findings suggest that diseases in prey have different effects on the proposed system, which can both stabilize or destabilize it. On the other hand, the wind flow represents a significant abiotic factor in the environment that affects the predation process. It is found that increasing the wind flow causes the extinction of the predator, which means the effect of wind flow acts as a bar to the search for food and decreases the efficiency of predators.
Semi-Markovian analysis of the prognosis of breast cancer between diagnosis and treatment initiation in Kenya: A case study of two counties
Breast cancer is a major health burden not only globally. It is the most commonly diagnosed type of cancer globally and in Kenya. In 2022, 7,243 new cases of breast cancer were reported accounting for approximately 16.2% of all cancer cases diagnosed with a mortality rate of 11.6% which translates to 3,398 deaths. This study aimed to determine the prevalence and analyze female breast cancer (FBC) prognosis between diagnosis and treatment, taking a case study of two counties in Kenya. Data for this study was obtained from two cancer registries in two county hospitals with a sample of 300 health records. After data cleaning, 150 records were eligible for analysis. Key variables of interest in the study were staging information of FBC at diagnosis and treatment, time taken between diagnosis and treatment, as well as the waiting time before transiting to the subsequent stage. One of the approaches that can be used to gain insight into how breast cancer progresses over time is the application of semi-Markov analysis which was used to analyze the prognosis of breast cancer in two counties in Kenya. This was obtained by determining the prevalence of FBC at diagnosis and at treatment and finding the transitional probabilities between different cancer states. The results of the analysis showed that FBC stage III was the most prevalent at diagnosis and treatment initiation with a prevalence of 36% and 34.7% respectively. The probability of remaining at stage II or stage III after diagnosis was found to decrease with the increase in the waiting time before treatment initiation. The results outline the necessity of timely diagnosis and initiation of interventions, which may help in clinical decision-making, resource allocation and inform public health policies.
Fourier series nonparametric regression estimator for modeling status of unmet need in East Java Province in 2023
In recent years, the Estimator of Fourier Series Nonparametric Regression (FSNR) for quantitative data has generated a lot of attention. In practice, though, there is frequently a correlation between predictor and response, with categorical data serving as the response. Only certain techniques are used in some of the methodologies created today to address the health case of qualitative response data. No previous study can handle health data using FSNR estimator. This study presents a novel approach FSNR estimator with response variables in the form of categorical data specifically within the context of public health research. The research methods used are theoretical and application studies. The FSNR estimators method for categorical data assumes a relationship between the logit function and predictor variables that has a repeating pattern. The Newton-Raphson technique and MLE were used to obtain the FSNR estimators. To apply this method, we used application data status of unmet need in East Java Province in 2023. The unmet need rate in East Java was quite high, reaching 12.97 percent, while the target is 11.74 percent. Because of the lower deviance value, greater AUC, and Press's Q values, the results show that the FSNR offers much superior estimation results and accuracy for data applications.
Allee and fear effects in prey-predator dynamics: stability analysis and optimal harvesting
This study incorporates the Allee effect and the fear effect into a predator-prey model. We investigate how these factors, along with fishing pressure, influence the population dynamics of both predator and prey. The analysis begins by establishing the positivity and boundedness of solutions, ensuring the populations remain within realistic ranges. Stability analysis of the interior equilibrium point, where both populations coexist, reveals the system’s resilience to disturbances. Furthermore, we explore optimal fishing strategies that balance maximizing long-term profit with maintaining sustainable populations. Finally, numerical simulations conducted validate the theoretical predictions.
Predictive risk modeling for outcomes of ischemic and hemorraghic stroke using feed-forward neural networks
Stroke is one of the leading causes of mortality and long-term disability worldwide, with ischemic and hemorrhagic strokes being the two primary subtypes. Accurate prediction of stroke outcomes is crucial for early intervention and improved patient management. In this study, we develop a predictive risk model using a Feed-Forward Neural Network (FFNN) to classify and assess risk factors associated with ischemic and hemorrhagic strokes. The model is trained on a dataset consisting of clinical, demographic, and physiological variables to distinguish between stroke subtypes and predict patient prognosis. Performance is evaluated using accuracy, sensitivity, specificity, and the area under the ROC curve (AUC-ROC). The results demonstrate that the FFNN model achieves high predictive accuracy (95.87%) for training and (80%) for testing in classifying stroke types and estimating risk. This study highlights the potential of deep learning techniques in enhancing stroke risk assessment and decision-making in clinical practice.
The asymmetric volatility model of Indonesian crude oil price with artificial neural networks hybridization
Volatility is a measure of changes in security prices that can be used to measure investment risk. Volatility can be detected through a variance model that contains heteroscedasticity effects in the form of ARCH/GARCH. If volatility contains asymmetric effects, it can be overcome by exponential and threshold models, namely the EGARCH and TGARCH models. Although it can overcome heteroscedasticity and asymmetric effects, this variance model needs to maintain model stability and accuracy levels, so the neural networks of multilayer perceptron (MLP) and radial basis function (RBF) are proposed as a neuroinformatics approach. This study uses Indonesian crude oil price (ICP) data from January 2011 to December 2024. The modeling results show that the variance model with the hybrid MLP and RBF neural networks approach is able to provide better accuracy, although the EGARCH and TGARCH models can still overcome asymmetric volatility. The hybrid neural networks approach can provide more precise information on variance models that can be used as an alternative in investment decisions related to ICPs that have an asymmetric volatility structure with irregular price fluctuations.
Analysis of special index of stunting treatment through confidence interval of longitudinal semiparametric spline model parameters
Stunting is a major concern in many nations, including Indonesia, and it has long-term implications for human resource quality. The Special Index of Stunting Treatment (SIST) is one of the social population problems that can be modeled with regression. The combination of parametric and nonparametric regression techniques is known as a semiparametric regression. This study used longitudinal data, obtained from repeated observations within a certain time span on the same individual in sequence. This study's estimation method makes use of a truncated spline, which has great flexibility and statistical interpretation. In the statistical inference of the parameter, the calculation of the confidence interval is crucial. Providing an estimated range for a population parameter based on two boundary points enables quantification of the level of confidence in the accuracy and reliability of the estimate. Six dimensions are formed in the acceleration of stunting reduction: health, education, nutrition, housing, food, and social protection. Results of the confidence interval estimation of truncated semiparametric spline regression parameters on longitudinal data. The optimal model was obtained using three knot points, resulting in a minimum GCV of 12.7066, an MSE of 2.0225, and R2 93.66%. This study shows that this model is feasible and the predictor variables have a negative and positive influence on the Special Index of Stunting Treatment (SIST).
Stability and bifurcation analysis of a class of delayed fractional differential equations describing the dynamics of HIV
In this paper, we propose a new delayed fractional-order model that describes the dynamics of human immunodeficiency virus (HIV). The proposed model incorporates three transmission modes, two types of infected cells, the adaptive immunity exerted by antibodies and CTL cells, two delays, one in viral production and the other in the activation time of antibodies, as well as four therapeutic parameters to represent different aspects of the therapy and the effect of memory described by Caputo fractional derivative. Additionally, we determine the equilibrium points and analyze their global stability with respect to specific threshold parameters. Moreover, we explore the existence of the Hopf bifurcation, demonstrating that the immune delay is the primary factor responsible for its occurrence.
Graph-theoretical analysis of peripheral molecular descriptors for phloroglucinol used in the treatment of spasmodicpain
This article presents a detailed mathematical analysis and computational approach to peripheral-based molecular descriptors of the phloroglucinol molecular graph, focusing on their relaionship with key chemical properties. Phloroglucinol, a polyphenolic compound with significant biochemical and pharmacological relevance, can be represented graph-theoretically, where molecular descriptors provide crutial insights into its structural and chemical behaviour. Using graph theory, we compute mostar index, that capture peripheral molecular features. The study highlights how these descriptors relate to phloroglucinol,s chemical properties, such as stability, reactivity, and potential biological activity. Furthermore, computational algorithms are employed to validate and optimize descriptor calculations, offering a comprehensive framework for studying the molecular characteristics of phloroglucinol. The findings contribute to the broader understanding of molecular graph theory applications in chemistry and pharmaceutical sciences.
CRCDKD: A novel architecture for medical skin cancer classification on the imbalanced HAM10000 dataset
Addressing the critical challenge of imbalanced data in medical skin cancer classification, this paper proposes a novel Categorical Relation-Preserving Contrastive Decoupled Knowledge Distillation (CRCDKD) framework tailored for the HAM10000 dataset, a widely recognized benchmark for skin disease image analysis. To mitigate biases toward majority classes and enhance diagnostic reliability across all categories, the architecture integrates a mean-teacher paradigm with categorical relation-preserving contrastive learning, augmented by a newly proposed Decoupled Mean Teacher Knowledge Distillation (DMTKD) module. This synergistic approach decouples feature learning and knowledge distillation, enabling dynamic optimization of performance trade-offs between underrepresented and dominant categories while accelerating model convergence. The results demonstrated that the proposed framework achieved a balanced multiclass accuracy (BMA) of 84.45%, alongside an overall accuracy of 89.41%, precision of 83.27%, recall of 84.85%, specificity of 97.50%, F1-score of 83.39%, and an area under the curve (AUC) of 98.41%, surpassing state-of-the-art techniques. These metrics highlight significant improvements over existing methods, particularly in minority-class accuracy and balanced performance (BMA), with the DMTKD module offering unprecedented flexibility to adapt decision boundaries. The proposed framework not only advances skin cancer detection for imbalanced medical datasets but also introduces a generalizable paradigm for fairness-aware deep learning in healthcare applications, ensuring robustness across diverse clinical scenarios.
A comparative study of GWR, HLM, and HGWR for modeling childhood stunting in Indonesia
Childhood stunting is an important biological and public health problem in Indonesia, with far-reaching consequences for cognitive development, disease risk and economic productivity. The prevalence of stunting shows considerable spatial and contextual differences, which are influenced by local socioeconomic and environmental conditions. We compare three regression models, Geographically Weighted Regression (GWR), Hierarchical Linear Model (HLM), and Hierarchical Geographically Weighted Regression (HGWR), to represent this complexity with the observations of 514 districts nested in 34 provinces in Indonesia. The outcome variable is the prevalence of stunting (%), with district-level predictors of poverty rate, education, sanitation, immunisation, and access to clean water and province-level predictors of HDI, health budget per capita, and prevalence of malnutrition. All Models capture Different dimensions of structure: GWR for spatial non-stationarity, HLM for hierarchical nesting, and HGWR for both. Model assessment was based on AIC, RMSE and adj. R2 values. The best model for overall goodness of fit was HGWR (AIC = 3196.563; RMSE = 5.159; Adjusted R² = 65.73%), in which it showed high performance to model spatially-structured and hierarchically-nested health themes. This research highlights the value of spatial-hierarchical models and encourages support for the soundness of HGWR as an effective paradigm to support targeted public health interventions in geospatial epidemiology.
Analysis of maternal mortality using geographically weighted Poisson regression with spline truncated estimator
This study analyzes maternal mortality in South Sulawesi in 2020 and identifies the determining factors utilizing the Spline Truncated approach in the Geographically Weighted Poisson Regression method (GWPR-ST). This approach builds on nonparametric regression to manage spatial heterogeneity by calculating local parameters at each observation site. Maternal mortality data often follows a Poisson distribution and exhibits overdispersion, which violates the equidispersion assumption of standard Poisson regression. The GWPR-ST method effectively handles overdispersion while accounting for spatial variability. The model estimation uses 1, 2, and 3 knot points, with the Gaussian Kernel as the weighting function. The selection of optimum bandwidth is carried out with Generalized Cross Validation (GCV). The most suitable model is obtained with an order of m=1 and h=3 knot points, resulting in an R-squared value of 80.04. This shows that the GWPR-ST model accounts for 80.04% of the impact of predictor variables on the maternal mortality rate response variable. The influential predictor variables vary across locations, allowing them to be classified into four groups based on the significant predictor variables. These findings provide valuable insights for targeted public health interventions and demonstrate the effectiveness of GWPR-ST in modeling spatially heterogeneous count data with overdispersion.
Enhancing breast cancer detection using machine learning on data from Cuban women
Breast cancer is becoming as the predominant cause of cancer-related mortality among women globally. Accurate and early diagnosis in detecting the presence of breast cancer can bring a positive impact in reducing mortality rates. This research explored the capabilities of a machine learning approach in detecting the presence of breast cancer in patients undergoing screening based on patient background parameters. This study utilized a publicly available dataset entitled Breast Cancer Risk Factors in Cuban Women obtained from Mendeley Data. This research contribution is the exploration and experiment of various machine learning models, such as support vector machine (SVM) using various kernels as our proposed model, logistic regression as our baseline model, and random forest as a comparison model with the best model in previous research that provided this dataset, with the result that our methodology, especially in handling preprocessing data and feature engineering, can improve most tested machine learning models to achieve perfect scores (100% accuracy, precision, recall, and F1-score), except for the SVM with radial basis function (RBF) kernel.
Modeling and analysis of an SIQRC system with fractional differential equations, cross-immunity, and inhibitory effects
This paper presents an SIQRC epidemic model formulated using fractional differential equations, incorporating a logistic growth rate and accounting for cross-immunity effects. The model further integrates inhibitory factors to assess their impact on disease transmission. We establish the non-negativity and boundedness of solutions, ensuring the biological feasibility of the model. We calculated the basic reproduction number, and the stability of equilibrium points is also analysed. Numerical simulations support the analytical findings highlighting the influence of the fractional order α on disease prevalance. Further, we investigate the influence of various parameters and inhibitory effects on disease prevalence. Additionally, we used Partial rank correlation coefficients and Latin hypercube sampling for global sensitivity analysis to determine key parameters affecting disease dynamics. This study provides valuable insights into the control and mitigation strategies for multi-strain infectious diseases.
Analysis of maternal mortality rate using multivariate adaptive generalized Poisson regression spline
Maternal mortality is an essential indicator for assessing public health levels and the quality of healthcare services in a country. In South Sulawesi Province, maternal mortality reached 198 cases in 2021, increasing from 133 cases in 2020. This high mortality rate requires urgent attention to identifying contributing factors. Maternal mortality data is discrete categorical data that follows a Poisson distribution and experiences overdispersion. This nonlinear and random data pattern makes it more suitable for nonparametric analysis. The appropriate method for these data characteristics is Multivariate Adaptive Generalized Poisson Regression Splines (MAGPRS). This study aims to identify the factors influencing maternal mortality in South Sulawesi Province using the MAGPRS method. The best model was obtained with a combination of basis function (BF) of 20, Maximum Interaction (MI) of 3, and Minimum Observation (MO) of 2, yielding a Generalized Cross-Validation (GCV) value of 0.000046683 and an R-Square of 99.30%, indicating high model accuracy. The findings reveal that the most influential factors include the percentage of pregnant women in the K4 program (X1), those receiving Td3 immunization (X5), postpartum mothers receiving vitamin A (X4), deliveries in healthcare facilities (X3), and pregnant women in the K1 program (X2).
Local bifurcation analysis of an ecosystem under the effect of toxicity and self-defense
The local bifurcation phenomena in a nonlinear ecosystem model incorporating toxicity effects and species' self-defense strategies are explored in this work. The influence of the ecological parameters on the stability of the equilibrium point is investigated. Bifurcation analysis has significant importance because it reveals the changes that occur at the equilibrium points, as well as how specific parameters affect the system. This paper achieved sufficient conditions that ensure the appearance of local bifurcation (LB), pitchfork bifurcation (PFB), transcritical bifurcation (TB), saddle-node bifurcation (SNB), and Hopf bifurcation (HB) of the system, which consists of prey, middle predator, and top predator with toxin effects and self-defense in the ecosystems. Sotomayor's theorem and Hopf bifurcation conditions help characterize the system's sensitivity to parameter variations. We observed that near the first equilibrium point, PFB occurs. At the free top predator equilibrium points, there is TB, and for the positive equilibrium points, there is SNB. HB close to the positive equilibrium point has also been studied. Numerical analysis is employed to validate the primary theoretical findings and to illustrate how alterations in parameters have a substantial impact on maintaining biodiversity and ecological balance.
Stability analysis and asymptotic behavior of a stochastic delayed SIRS epidemic model with a class of nonlinear incidence rates
This paper deals with a stochastic version of a deterministic delayed SIRS (Susceptible-InfectiveRemoved-Suceptible) epidemic model with nonlinear incidence rate. The stochastic model is obtained by taking into account random perturbations in the contact rate β due to environmental variations. We assume that the stochastic perturbation intensity is proportional to the number of infectious. Firstly, the existence of a unique global positive solution of the stochastic differential equations with delay describing the model is proved. Then, the stability of the disease-free equilibrium point is established under suitable conditions on the parameters of the model. We also study the asymptotic behaviour of the solution when the disease-free equilibrium (DFE) is unstable. Finally, numerical simulations are introduced to support our results.
Computational optimization of fractional-order influenza SIR epidemic modeling using two effective techniques
In this study, we employ two efficient approaches, the q-homotopy analysis transform method and the Predictor-Corrector method to find and analyze the solution for the fractional order influenza SIR epidemic model. In recent times, numerous innovative definitions of fractional derivatives have been proposed and employed to construct mathematical models for an extensive array of complex problems, including nonlocal effects, memory, and history. We implement the Caputo fractional derivative for the considered SIR epidemic model of influenza which is characterized by ordinary differential equations of nonlinear form. The q-homotopy analysis method and the Laplace transform are combined to form the basis of q-homotopy analysis transform method. The outcomes of the methods under consideration can be found as a quickly convergent solutions. To illustrate the accuracy, speed, and high order of convergence of the q-homotopy analysis transform method, its solution is compared to that produced by the Residual power series method and fourth-order Runge-Kutta method. The 3D plots, graphs and numerical results express the physical representation of the considered model. It exhibits that the Predictor-Corrector approach and the q-homotopy analysis transform method are meticulous, reliable, and effective to examine the suggested influenza SIR epidemic model and a few other fractional order differential equations in epidemiology. The details of the solution behavior are provided by this analysis, which ensures accurate epidemic predictions. In addition to improving epidemic modeling, this new approach is a more precise tool for forecasting and planning public health. The paper establishes an evaluation for fractional epidemic models and demonstrates the utility of the methods in the context of disease transmission.
Longitudinal data analysis by nonparametric bi-response spline truncated regression model
This study aims to construct a growth model for toddlers based on longitudinal data using a nonparametric bivariate response truncated spline regression approach. The data used consisted of routine toddler weighing records from the Integrated Health Post in Bontosunggu Village, South Bontonompo Sub-District, Gowa Regency, encompassing age, body weight, and height of toddlers from January to December 2021. The analysis was conducted by developing two regression models for each response variable, namely body weight and height, using four knot points (12, 24, 36, and 48 months), and parameter estimation was carried out using the Ordinary Least Squares (OLS) method. The analysis results indicate that the growth of toddlers’ weight and height does not follow a linear pattern with age but rather displays a change in growth rate at specific age points. This model provides a more realistic and flexible depiction of growth and can serve as a useful tool for monitoring the nutritional and health status of early childhood populations.
Public health interventions for fractional optimal control of Buruli ulcer
Buruli Ulcer, a devastating skin disease caused by Mycobacterium Ulcerans, poses considerable public health challenges in endemic areas. This article focuses on the use of fractional optimal control theory to prevent the spread of Buruli ulcers via integrated public health interventions. We formulated a mathematical model using the Atangana-Baleanu-Caputo fractional order derivative operator. We investigated the model’s existence and uniqueness and presented numerical simulations using the predict-evaluate-correct-evaluate (PECE) method of Adam-Bashforth Moulton. We also study the fractional optimal control problem (FOCP) to minimize the spread of the disease in the endemic regions. We employ the Fractional Pontryagin’s Maximum Principle (FPMP) and implement the forward-backward method to determine the extremals of the problem. Four control strategies were implemented: promoting health education on the use of protective clothing, enhancing vaccination rates, improving treatment protocols for infected individuals, and spraying insecticides to reduce water-bug populations. After examining the optimal control dynamics of the Buruli ulcer transmission model via multiple simulations with and without control, we discover that there is a substantial decrease in the population of infected humans and the water-bug population. Hence we conclude that the best strategy to implement is by applying all the control strategies suggested.
The role of saturated incidence and treatment rates on the dynamics of epidemiological model
This paper examines an epidemic model of the SEIR type that was created to account for the impact of immunization campaigns and saturated therapy. To determine the effects of inadequate health care and the efficacy of vaccinations in halting the spread of infection, the model was mathematically examined. Both local and global stability were examined, and equilibrium points were computed. Additionally, the pattern may exhibit inverse branching, according to the research, suggesting that the sickness can persist even when R0<1. A sensitivity study was used to determine which aspects of the proliferation dynamic were most crucial. Numerical findings corroborate theoretical predictions and highlight the need to combine medication and vaccination as effective epidemic management strategies.
Multidisciplinary approach to in vitro propagation of Coelogyne pandurata Lindl. from Kalimantan: synergistic effects of naphthalene acetic acid and yeast extract with a mathematical biology perspective
This study investigates the synergistic effects of Naphthalene Acetic Acid (NAA) and yeast extract on the in vitro propagation of Coelogyne pandurata (black orchid) using a multidisciplinary approach that combines biological experimentation and statistical analysis. The research aimed to optimize vegetative growth, specifically shoot, leaf, and root development, by applying different concentrations of NAA (0, 1, 3, and 5 mg/L) and yeast extract (0, 0.5, 1, and 1.5 g/L). Data analysis involved Pearson correlation, Kruskal-Wallis test, and hierarchical cluster analysis. The Pearson correlation matrix revealed a strong positive relationship between shoot and leaf growth (r = 0.93), indicating that increased shoot formation was associated with leaf development. A weaker correlation was observed between shoot and root growth (r=0.39), and a moderate correlation was found between leaf and root growth (r=0.55). Statistical analysis using the Kruskal-Wallis test showed significant differences in root number (pvalue=0.04) among various NAA treatments, with the 1 mg/L NAA concentration resulting in the highest root number. Yeast extract concentration also significantly influenced shoot (pvalue=0.03) and root (pvalue=0.03) development, while leaf number remained unaffected (p = 0.07). Cluster analysis using Ward’s method revealed distinct treatment groups based on growth patterns. Treatments with moderate yeast extract concentrations (1–1.5 g/L) clustered together, showing enhanced shoot and root growth, while high concentrations of NAA combined with yeast extract resulted in suppressed root development. These findings indicate that a balanced combination of NAA and yeast extract optimizes the vegetative growth of black orchids. This study contributes to the understanding of growth regulation in Coelogyne pandurata and offers insights for improving orchid propagation in vitro.
Harvesting of a predator-prey model with two effort functions and Holling type IV response function
This study presents a mathematical model describing a three-species interaction in a marine ecosystem, involving two prey populations distributed across protected and exploited zones and a single predator species. The model is grounded in the Holling type IV functional response and incorporates two dynamic fishing effort functions governed by their own evolution equations. Unlike traditional static-effort frameworks, our approach reflects adaptive economic behavior over time. We investigate system dynamics through equilibrium analysis, local and global stability assessment using Lyapunov techniques, and derive an optimal harvesting strategy using Pontryagin’s Maximum Principle. Numerical simulations illustrate how spatial management and effort adaptation jointly influence sustainability outcomes, offering insights for marine resource governance under complex ecological and economic feedbacks.
Machine learning based hydrological model: deep feed forward neural network (DFFNN)
This study applies the Deep Feed Forward Neural Network (DFFNN) model to forecast the number of rainy days in Indonesia, a tropical country characterized by significant seasonal rainfall variations. The data used includes daily rainfall data from the Juwata Tarakan Meteorological Station over the period from 2014 to 2024. DFFNN was chosen for its ability to handle non-linear relationships and temporal dependencies within complex time series data. Based on performance evaluation metrics such as MAPE, MSE, and RMSE, the model with a 4-hidden-layer architecture and a 4-5-3-5 neuron configuration, standardized using Z-Score, showed the best performance compared to other model combinations. The forecasting results reveal a seasonal pattern consistent with tropical rainfall cycles, with peaks in rainfall occurring from January to March and a decline observed between May and August. The model proved capable of providing accurate predictions for the number of rainy days, making it suitable for supporting early warning systems in mitigating natural disaster risks such as floods and landslides. However, the study also identified several limitations, particularly in the selection of input variables, hyperparameter tuning, and network architecture choices, which influence model performance. Therefore, further research is recommended to optimize these aspects to enhance prediction accuracy and stability in weather forecasting and disaster management.
Rainfall forecasting using extreme gradient boosting
Rainfall is an important factor affecting the agricultural sector, especially in areas such as Grobogan Regency, Central Java, which is one of the national rice barns. Rainfall uncertainty often leads to crop failure due to drought or flooding, which is caused by inaccurate rainfall predictions. This research aims to build a dasarian rainfall forecasting model using the Extreme Gradient Boosting (XGBoost) method. The data used is ten-day (decadal) rainfall data from January 1991 to February 2025. The research steps start from data preprocessing which includes lag and seasonal feature creation, hyperparameter determination and hyperparameter tuning, and model evaluation. After conducting hyperparameter tuning to find the best model, the best model was found with n_estimator 448, learning rate 0.14, max_depth 3, min_child_weight 1, subsample 0.71, colsample_bytree 0.97, gamma 5.1, alpha 3.8, and lambda 8.89. The model formed is then evaluated using SMAPE (Symmetrical Mean Absolute Error) for test data of 36.48%. From the model formed, forecasting is carried out and the forecasting results can be utilized as a basis for decision making in agricultural planning.
Optimising plant epidemic control: a mathematical model integrating susceptible and infectives plants, and herbivores with pesticide intervention
This work presents and analyses a deterministic mathematical model incorporating herbivores and plant populations, with pesticide application as a control measure. There are three distinct populations under consideration: susceptible and infected plants, as well as herbivorous population. Our model's goal is to analyse the interactions and dynamics of these populations. By analysing their behaviour, we can gain insight into the ecological processes that regulate their growth and survival. The model administers pesticides as a control measure to both susceptible and infected plants. Furthermore, given that herbivores have the potential to consume pesticide-sprayed plants, we can observe an interaction between herbivores and pesticides. The primary goal of pesticide application is to mitigate disease transmission among plant populations. To verify the biological validity and precisely defined characteristics of the model, we assess the system's permanence and examine its positivity, boundedness, uniqueness, and existence of solutions. The determination of the infection's basic reproduction number (R0) and observation of the disease-free equilibrium state reveal that it is locally asymptotically stable when R0 is less than unity, but unstable otherwise. In addition, we conduct sensitivity analysis on the basic reproduction number and use Pontryagin's Minimum Principle to determine a necessary condition for the existence of optimal controls. Finally, we perform numerical simulations using the MATLAB software to compare the analytical results. In summation, the findings yielded by this analysis are innovative and substantial, thereby constituting a meaningful addition to the body of knowledge in theoretical ecology.
Computational simulation of energy-based molecular characteristics and their statistical evaluation for anti-blood medicines
Cancer is a medical condition characterized by the abnormal growth and reproduction of cells in a specific region of the body. Blood cancer is a form of malignancy that originates in the bone marrow, the vital site where blood cells are produced. In this article, QSPR analysis on anti-cancer drugs was made with the implication of various energies. The results highlight the immense potential of energies as a valuable tool for drug discovery and design within the realm of cancer treatment. This study showcases the significant role that graph theory and energies play in advancing the development of anti-cancer drugs. Furthermore, the findings underscore the importance of employing quantitative structure-property relationship (QSPR) analysis in this domain. Certain energies exhibit a very high correlation with physical and chemical characteristics of drugs. Although the values of p are significant for almost all pharmacological properties. This analysis revealed that the graphical energies determined in this article could assist chemists and other pharmaceutical professionals in developing novel medications. This technique aims to offer a low-cost way to identify the physicochemical characteristics of medications.
A simulation study on the impact of censoring on standard errors in the clustered joint model
This simulation study rigorously evaluated the impact of censoring on standard error (SE) estimation in clustered joint models for longitudinal binary and survival outcomes. Joint models were vital in biomedical research for analysing interdependent repeated measures and event times, but their performance in clustered settings (e.g., multicenter trials) under censoring remained under explored. We focused on scenarios like adolescent HIV studies, where binary viral load suppression (longitudinal) and time to treatment interruption (survival) were modelled jointly with shared random effects to account for within-cluster correlation. Using Monte Carlo simulations (200–1000 replications) with 10 clusters of 20 subjects, we systematically varied right-censoring rates (5%–35%), cluster sizes, and random-effects structures. Performance metrics including bias, root mean squared error (RMSE), empirical standard errors (ESE), asymptotic standard errors (ASE), and coverage probabilities (CP) were compared. Results revealed that censoring significantly distorted SE estimation, with ASE increasingly underestimating ESE for key parameters as censoring intensified. For WHO stage parameters (e.g., β2, β3), ASEESE agreement held reasonably until 20% censoring, but deteriorated thereafter. The ART regimen parameter (γs) exhibited substantial bias and RMSE inflation beyond 20% censoring (e.g., bias: 0.0675, RMSE: 0.1441 at 30% censoring), with CP falling to 89.5%. Conversely, age parameters (γa) showed reduced bias under higher censoring. Variance components (log(σu), log(σv)) displayed significant ASE-ESE discrepancies at all censoring levels. We identified a critical threshold near 20% censoring, beyond which inference reliability declined markedly for treatment-related parameters. Spline-smoothed error trends further illustrated parameter-specific sensitivities. These findings cautioned against relying solely on asymptotic SE approximations in high-censoring or complex clustered designs and underscored the need for robust variance estimation. The study provided practical guidance: research focused on clinical covariates (e.g., ART) should limit censoring below 20%, while demographic parameters tolerated higher rates.
The role of prey vigilance, cannibalism, and hunting cooperation on prey-predator dynamics
Examining a prey-predator system that includes intricate behaviors like cannibalism, prey vigilance, and predators' hunting coordination is necessary to comprehend the complex dynamics of natural systems. These factors significantly affect population stability, persistence, and environmental equilibrium. Consequently, a novel prey-predator model with these features is proposed for study in this paper. Using the Lyapunov method of equilibria, the requirements for global stability, local stability with the aid of the linearization approach, and the existence of equilibria were established. Local bifurcation types in the sense of Sotomayor and Hopf bifurcations were detected. Finally, numerical simulations are used to comprehend how changing the parameters affects the model's dynamics.
Stability and bifurcation analysis of prey-predator model with SIS type of disease and anti-predator property
A prey-predator model involving anti-predator behavior and fear of predation with disease in a predator is proposed and studied. The main objective of this study is to find out the influence of anti-predator and fear on the population dynamics of the model in the presence of disease. It is assumed that the disease in the predator is of the SIS type. For this purpose, a mathematical model with a Holling- type II functional response was proposed and analyzed. The existence conditions and stability of different equilibrium points for the model were analyzed to determine the qualitative behavior of the model. Investigations of local bifurcations had been conducted. It can be shown that the results of numerical simulations are consistent with analytical results.
Bayesian estimation for the Lomax distribution: comparing loss functions under different priors
This study aims to estimate the shape parameter (𝜃) of the Lomax distribution with a known scale parameter (β) using a Bayesian approach. Three Bayesian Loss Function methods are applied: Square Error Loss Function (SELF), Entropy Loss Function (ELF), and Precautionary Loss Function (PLF). The priors used include the conjugate Gamma prior and the non-informative Jeffrey prior. The estimation was conducted on simulated data with shape parameters (𝜃 = 1.3 and 1.5) and varying sample sizes (n = 30, 150, and 300). The estimation process involves constructing the posterior distribution by combining the prior distribution with the likelihood function of the Lomax distribution. The estimated parameters are evaluated using Akaike Information Criterion (AIC), corrected AIC (AICc), and Bayesian Information Criterion (BIC) to determine the best method under various conditions. Results indicate that the Bayesian SELF method provides the best estimation with the smallest AIC, AICc, and BIC values for small sample sizes (n = 30), regardless of whether the Gamma or Jeffrey prior is used. For larger sample sizes (n = 150 and 300), the Bayesian PLF method performs better. The conjugate Gamma prior consistently produces more stable estimates compared to the non-informative Jeffrey prior. This research highlights that the optimal choice of Bayesian Loss Function depends on the sample size and the type of prior. These findings provide valuable insights for improving parameter estimation methods for the Lomax distribution, which has wide applications in heavy-tailed data analysis in fields such as finance, queuing theory, and internet traffic modeling.
Topological data analysis in EEG signal processing: a review
Electroencephalogram (EEG) is a non-invasive technique that measures the brain's electrical activity from the cerebral cortex. EEG has been adopted in many studies for disease diagnosis, brain state recognition, and perception evaluation due to its high temporal resolution and low cost. Conventional data analysis methods such as traditional statistics and machine learning, suffer from several limitations, including being sensitive to artifacts when applied to EEG signal processing. As an alternative to these approaches, topological data analysis (TDA) enhances the EEG analysis by focusing on the robust topological invariants in EEG data. The rapid development of the TDA method generates a variety of studies with different TDA-based EEG processing pipelines tailored to diverse research objectives. A comprehensive review of these studies is necessary to serve as a guide for practitioners to gain deeper insight into EEG processing with TDA. This review also identifies the strengths, weaknesses, and future directions of TDA in EEG studies.
Approximate Bayesian computation for the Ross-Macdonald model of malaria transmission
The Ross-Macdonald model remains a key component in understanding the dynamics of malaria transmission, representing the complex interactions between mosquito and human populations through a coupled system of ordinary differential equations (ODEs). Parameter estimation for this model presents significant challenges due to the intractable likelihood function and multiple uncertain parameters that govern transmission dynamics in epidemiology. This study implements Approximate Bayesian Computation with Sequential Monte Carlo (ABC-SMC) methods to perform parameter inference on the Ross-Macdonald model. We demonstrate that ABC-SMC provides a robust framework for parameter estimation while accounting for model uncertainty and parameter correlations. Our analysis reveals critical information on the sensitivity of the basic reproduction number R0 to various epidemiological parameters. The methodology presented offers a practical approach to the development of evidence-based policies and provides uncertainty quantification essential for robust decision making.
Mathematical modelling to assess the impact of a hypothetical vaccine on the dynamics of human onchocerciasis
Human Onchocerciasis (River Blindness) is a neglected tropical disease with no cure. Over the years, its control and elimination had relied on Ivermectin mass drug administration. However, some public health experts and other researchers have pointed out that Onchocerciasis complete elimination may not be achievable or may required a very long time with Ivermectin drug alone. Hence, the need for more research into other alternative control strategies to assist public health authorities. The aim of this study is to construct a mathematical model to examine the influence of a hypothetical vaccine as an additional control measure for the elimination of human Onchocerciasis. We computed the disease reproductive number with and without vaccination campaign and further derived a reduction factor by which a vaccination campaign will reduce Onchocerciasis spread in a community. The proposed model disease-free equilibrium is shown to be stable when the controlled Ro < 1. An equation for the disease endemic condition was derived and the conditions for the existence of two endemic equilibria when Ro < 1 or a globally asymptotically unique equilibrium when Ro > 1 were established. Local sensitivity revealed that black fly removal rate is the most significant parameter for controlling human Onchocerciasis. To examine the evolution of the model sub-classes, numerical simulations were carried out.
Stability of delayed general HIV-1 with cell-to-cell and inflammatory cytokines infection model with immune system response
In this paper, we propose a dynamical model for the immune system’s reaction to HIV-1 that includes three temporal delays distributed in the presence of inflammatory cytokines. The model contains six components: uninfected CD4+T cells, infected CD4+T cells, inflammatory cytokines, HIV-1 virus, CTLs, and antibodies. The model contains the general functions for the incidence rates of the healthy CD4+T cells with viruses, infected cells, and inflammatory cytokines. Moreover, the production/proliferation and removal/death rates of the virus and cells are represented by general functions, too. The model was developed to better understand HIV-1 infection by describing two immune responses (antibody and cytotoxic T lymphocyte (CTLs)), three forms of distributed time delays, and inflammatory cytokines in the context of an infection through cell-to-cell (CTC) transmission. First, the system’s basic properties were investigated; then the equilibria points of the system were determined. The reproduction numbers for the model have been calculated and investigated, too. The model has five reproduction numbers, basic one (ℜ0), CTLs immune response (ℜ1), antibody immune response (ℜ2), CTLs immune competitive (ℜ3), and antibody immune competitive (ℜ4). Using the Lyapunov approach and LaSalle’s invariance principle, we have demonstrated the global asymptotic stability of all equilibria under a set of restrictions on the general functions and the threshold parameters. The numerical simulations has been performed to demonstrate the theoretical results. By adding a time delay for the model can reduce the quantities of free HIV-1 particles and infected cells while also dramatically raising the concentration of healthy CD4+T cells. However, the addition of CTC transmission raises the concentrations of infected cells and free HIV-1 particles while decreasing the concentration of healthy CD4+T cells.
Stochastic differential equations for SIR malaria model
This study develops a stochastic extension of the classical SIR malaria model to more realistically capture the dynamics of malaria transmission under environmental uncertainty. By incorporating Brownian motion into the deterministic framework, the model accounts for random fluctuations in transmission and recovery processes affecting both human and mosquito populations. The stochastic differential equations (SDEs) are solved using three numerical methods: Euler–Maruyama, Milstein, and Stochastic Runge–Kutta. Each method is evaluated for accuracy and reliability using error metrics such as Mean Absolute Deviation (MAD), Root Mean Square Error (RMSE), and the Anderson–Darling goodness-of-fit test. The Euler–Maruyama method demonstrates superior performance in approximating human infection and recovery dynamics, while the Milstein method provides a balanced estimate for both human and vector compartments. The study further introduces a novel convergence metric–Okwomi C∗–based on the Geweke diagnostic, enabling robust assessment of convergence in stochastic simulations. Simulation results show that stochastic models capture extinction and variability effects not evident in deterministic models, even when the basic reproduction number exceeds one. Overall, the integration of stochastic processes improves epidemic forecasting and informs more resilient malaria control strategies under uncertainty.
Multivariate adaptive bivariate regression splines (MABRS) binary response for modeling stroke and hypertension in RSKD Dadi City Makassar
Classification of health conditions with more than one correlated response variable is an important challenge in medical data analysis. This study proposes a Multivariate Adaptive Bivariate Regression Splines (MABRS) approach to classify stroke type (ischemic vs. hemorrhagic) and hypertension status simultaneously. Utilizing clinical data from stroke patients, the MABRS model was built based on the optimal parameter combination for each response. The results showed that the stroke type classification achieved a fairly good performance (accuracy 76.82%), with the most influential variables being obesity, hypercholesterolemia, and diabetes mellitus. In contrast, the hypertension classification model performed poorly (51.21% accuracy), although diabetes mellitus, gender, and age were identified as the main predictors. The MABRS approach has the advantage of capturing nonlinear relationships and interactions between predictor variables, while considering the correlation between two binary response variables in a unified model framework. These findings confirm the potential of MABRS in uncovering complex relationships between clinical variables and supporting data-driven medical decision-making, particularly in the management of comorbidities in stroke patients.
Improving exchange rate prediction accuracy with 1D-CNN-BiGRU and walk forward analysis
This study was conducted to improve the accuracy of forecasting the exchange rate of the Rupiah against the Japanese Yen, which was crucial for economic actors in managing risks, enhancing investment efficiency, and supporting adaptive financial policies. The research aimed to develop a forecasting method with the lowest possible error rate (MAPE) to address the limitations of conventional models and provide more accurate insights for decision- makers. The method used was a hybrid approach combining a 1D-Convolutional Neural Network (1D-CNN) and a Bidirectional Gated Recurrent Unit (BiGRU), along with a walk-forward analysis strategy to capture trend patterns and short-term volatility in exchange rates. The results showed that the Hybrid 1D-CNN-BiGRU model effectively predicted exchange rate fluctuations for the next five days, achieving a MAPE value below 1%, indicating higher accuracy compared to previous approaches. The conclusion of this study was that the Hybrid 1D-CNN-BiGRU model was an effective forecasting method for the Rupiah-to-Yen exchange rate, providing a stronger foundation for economic actors in making currency transaction decisions. The main contribution of this research was the implementation of a combined method that had not been previously applied in exchange rate forecasting, opening new opportunities for further research in exploring other hybrid models to improve prediction accuracy in various economic and financial fields.
Optimal control strategy for a discrete-time mathematical modeling of water pollution
Water pollution is a major issue with serious consequences for human health and the environment, particularly in developing countries. It highlights that contaminated water is a source of waterborne diseases, such as cholera, and underscores the importance of integrating temperature variations into pollution management strategies. A discrete mathematical model is proposed, segmenting the problem into three compartments: at-risk water, polluted water, and the total sum of pollutants, accompanied by difference equations that represent their interactions. The challenge of optimal control aims to reduce pollutant concentrations through three approaches: awareness, purification, and source reduction. Numerical simulations conducted with MATLAB show that these interventions can significantly reduce water pollution. In conclusion, the article emphasizes that the application of mathematical modeling and optimal control strategies is crucial for mitigating the effects of pollution and proposing sustainable solutions for water management.
Mapping districts in West Java by under-five pneumonia indicators: an agglomerative hierarchical clustering study (Open Data Jabar 2023)
In West Java Province, Indonesia, pneumonia remains a major contributor to morbidity and mortality among children under five years of age. This study aims to employ an agglomerative hierarchical clustering approach to classify districts and cities based on indicators associated with under-five pneumonia. The analysis utilized secondary data from Open Data Jabar (2023), encompassing nine cities and eighteen districts. The variables considered included malnutrition prevalence, vitamin A supplementation coverage, incidence of low birth weight, DPT-HB-HIB 3 immunization coverage, the proportion of households practicing Clean and Healthy Living Behavior (PHBS), and the number of reported pneumonia cases. Euclidean distance was applied to compare five linkage methods, with the Single Linkage method selected for final clustering due to its highest cophenetic correlation coefficient (0.8681). The optimal clustering solution yielded four distinct profiles, ranging from regions with high PHBS coverage and immunization rates to those with low immunization coverage and high malnutrition prevalence. These findings provide an evidence-based framework for designing region-specific pneumonia prevention and control strategies targeting under-five populations in West Java.
Activation functions for deep neural networks
Deep Neural Networks are connectionist models composed of multiple layers of neuron-like computational units that try to simulate two fundamental aspects of human intelligence: i) learning from examples, and ii) generalizing the learned knowledge and skills to new and unseen examples. The design of such a model for any real-world application requires several steps, including the choice of an adequate architecture in terms of the number of layers, as well as the size, the type, and the activation function of each layer. This paper investigates the impact of activation functions on the overall performance of the network, which has remained underestimated until the early 2010s. The paper provides a brief historical review of recent literature, along with some practical recommendations for selecting the most appropriate activation functions according to each situation. To illustrate the studied problem, we also present some experimental results showing that a shallow neural network with appropriate activation functions may be more efficient than a deeper neural network using traditional and inappropriate functions.
The bifurcation conditions of Sokol-Howell prey-predator model involving fear and toxin
In this paper, the conditions of the occurrence of local bifurcation (LB) have been founded for a food- chain eco-toxicant model involving three species: prey, first and second predators, incorporating factors such as fear, as well as linear and nonlinear harvesting strategies, including two various functional responses (Lotka-Volterra and Sokol-Howell). This model features six equilibrium points (EPS), all of which are stable under appropriate conditions, the saddle-node bifurcation (SNB) appears near the positive point E5, transcritical bifurcation (TB) and pitchfork bifurcation (PB) occur near the points E2 and E3, while only a transcritical bifurcation takes place near the point E0, E1, and E4. Additionally, the Hopf bifurcation (HB) conditions near the positive equilibrium point (PEP) have been discussed. Finally, the numerical simulation for the hypothetical parameter set confirm our analytical findings about (LB) of this model.
A random forest algorithm for high-risk pregnancies prediction based on explainable artificial intelligence (XAI)
This study explores using the Random Forest (RF) algorithm with the Explainable Artificial Intelligence (XAI) approach to predict High risk in pregnant women. Preeclampsia is a disorder that occurs during pregnancy and is characterized by hypertension and organ damage. If not treated early, it can endanger both the mother and fetus. The RF algorithm was chosen because it can process complex data, resist overfitting, and achieve good classification performance. This study used 299 data points from pregnant women at the Community Health Centre Anak Air in Padang City. The SHAP (Shapley Additive Explanations) and LIME (Local Interpretable Model-agnostic Explanations) methods were then applied to determine the role of each feature in the prediction process. The results of the analysis show that the RF model effectively identifies pregnancy risk factors, particularly preeclampsia, such as age, body temperature, diastolic blood pressure (BP), blood sugar (BS), heart rate, and urine protein. The model achieved an accuracy of 78%, meaning that 78% of its predictions align with the actual data. The model was interpreted using SHAP and LIME. SHAP reveals globally important features, while LIME provides local explanations based on individual patient characteristics. Users, especially healthcare professionals, can more clearly and informatively understand the prediction results. This approach improves system accuracy and promotes clinical acceptance of AI-based predictive technology. The system can support the early detection of preeclampsia and more accurate decision-making in maternal healthcare.
Comparison of Bayesian dynamic linear and mixed effects interrupted time series models in assessing Uganda's neonatal mortality reduction since the SDGS onset
The study makes a comparison of two models used to assess Uganda’s effort in reducing neonatal mortality since the onset of the Sustainable Development Goals. These two models are Bayesian Dynamic Linear and Mixed Effects Interrupted Time Series Models. The study made use of secondary data obtained from the country’s Ministry of Health spanning from January 2015 to December 2023. To determine the most appropriate model, the study conducted both Robust tests of model diagnosis and K-fold cross-validation tests as a global measure of model comparison. The Bayesian Dynamic Linear Model outperformed the Mixed Effects Interrupted Time Series Model on three out of the four criteria considered to assess the two models. Besides having a higher Cross-Validated Root Mean Square Error, the Bayesian Dynamic Linear Model does better on robust tests and has a higher Cross-Validated Log Likelihood. Therefore, the Bayesian Dynamic Linear Model outshone Mixed Effects Interrupted Time Series Model as a preferred model for Neonatal mortality analysis amidst SDGs onset impact evolution, in alignment with the study’s methodological innovations and overarching research objectives.
A dynamical model of pneumonia transmission in children under five years with nutritional factors
Pneumonia is a major cause of death among children under five in Indonesia. This study presents a mathematical model to describe the transmission dynamics of pneumonia in this age group, incorporating the effects of nutritional status. A compartmental SVITR model (Susceptible–Vaccinated–Infected–Treated–Recovered or Immune) is formulated using a system of differential equations. Model parameters are estimated using the nonlinear least squares method and calibrated using pneumonia case data from Central Java Province, covering the period from January 2022 to December 2024. The mathematical analysis involves examining the positivity and boundedness of solutions, identifying equilibrium points, computing the basic reproduction number R0, and conducting local stability analysis. To identify key factors influencing disease spread, a sensitivity analysis is performed using the normalized forward sensitivity index. ​Numerical simulations indicate that when R0<1, the disease does not spread endemically and will eventually die out. Sensitivity analysis reveals that nutritional improvement has the most significant impact in reducing R0, followed by vaccination and antibiotic treatment, highlighting nutrition-based intervention as a key strategy for controlling pneumonia in under-five children.
Dynamical analysis and optimal control of a malaria transmission model with vaccination
This study develops and analyzes a compartmental model for optimizing malaria control strategies, with particular emphasis on the role of vaccination. The model captures key epidemiological dynamics, including resusceptibility, drug resistance, and vaccination, and incorporates three time-dependent control interventions: preventive measures, vaccination enhancement, and treatment efforts. The basic reproduction number is analytically derived to characterize the threshold conditions for disease persistence. Local and global stability analyses of the nonendemic equilibrium are carried out, providing theoretical assurance that the disease can be eradicated when the reproduction number is below unity. Parameter values are obtained from regional data and literature sources. A local sensitivity analysis based on elasticity indices identifies the most influential parameters affecting the basic reproduction number, notably the transmission rates between humans and mosquitoes and the treatment rate for drug-sensitive infections. Contour plots further illustrate the joint effects of key parameters on disease transmission potential. Optimal control strategies are derived using Pontryagin’s Maximum Principle and validated through numerical simulations. The results demonstrate that vaccination significantly reduces the number of infected individuals and enhances overall disease suppression, particularly when implemented alongside prevention and treatment controls. These findings underscore the importance of integrating vaccination with other public health interventions to design effective and cost-efficient malaria control programs.
Geographically weighted regression with Burr XII distribution for spatial analysis of diarrhea incidence in Surakarta City
Diarrhea is one of the leading causes of mortality in Indonesia. The persistence of this disease is closely related to spatial factors, such as environmental conditions and existing infrastructure. In Surakarta City, diarrhea was recorded as the most prevalent disease in 2024, with a 58% increase in cases compared to the previous year. The aim of this study is to apply the Geographically Weighted Regression (GWR) approach with the Burr XII distribution to model the spatial distribution of diarrhea cases in Surakarta. The study encompasses 54 urban villages and utilizes seven predictor variables, such as population density, elevation, distance to the nearest hospital, slope, proximity to rivers, distance to waste disposal sites, and rainfall. The Burr XII distribution was applied to handle the skewness frequently observed in health-related datasets such as diarrhea incidence, while GWR was used to generate location-specific parameter estimates. The developed model revealed clear spatial heterogeneity in how diarrhea cases are influenced by the predictor variables. Several factors, including population density, hospital distance, elevation, and river proximity, showed varying positive and negative effects depending on the geographical area. The results underline the necessity for targeted and well-coordinated public health measures to mitigate diarrhea risk, especially in communities with inadequate healthcare services and poor waste management systems.
Numerical modeling of HIV dynamics in CD4+ T-cells using fuzzy differential equations
In this study, we use fuzzy differential equations (FDEs) to present a mathematical model for the dynamics of HIV infection in CD4+ T-cells. Uninfected cells, infected cells, and viral particles, all of which are represented as fuzzy dynamical systems, are the three main components of the model. We use ρ-cut techniques to convert the fuzzy system into a corresponding crisp system of differential equations to analyze the spread and control of HIV. Equilibrium points and eigenvalue-based criteria are used in stability analysis. In addition, we derive approximate solutions using the fifth-order Runge-Kutta numerical approach. The suggested method provides a more adaptable and practical framework for understanding the dynamics of HIV infection in an environment of uncertainty.
Mathematical modeling of B-cell chronic lymphocytic leukemia and immune systems with therapy
A quantitative understanding of the dynamics of the immune system to treatment is important in planning treatment strategies, such as timing, dosing, and predicting the response to a certain treatment. In this context, mathematical modeling of the relationship between disease-causing cells and the immune system, along with treatment, is one of the effective methods. In this study, we establish a nonlinear dynamical system that models the interaction between B-cell chronic lymphocytic leukemia and the immune system with a chemo-drug. We examined behaviour of the solution of the system around equilibrium points via phase-space analysis. Local stability analysis is performed on the nonlinear system, and stability conditions are also derived in the Lyapunov sense. Finally, numerical results are obtained with respect to the cases, tumor size, parameter change, and drug addition.
A new gamma regression estimate of female body fat percentage: advanced statistical modeling
In this paper, a new gamma two-step shrinkage (GTSS) estimator is proposed for the gamma regression model to address the issue of multicollinearity. We derived the mean squared error (MSE) for the proposed estimator and defined the necessary and sufficient conditions for its superiority over five existing estimators. A comprehensive comparison is conducted between the proposed GTSS estimator and traditional maximum likelihood (ML) estimator, Liu estimator, and other conventional estimators, using a matrix mean squared error criterion. The results from the Monte Carlo simulation demonstrate the advantages of the proposed GTSS estimator under various conditions, particularly in the presence of severe multicollinearity. Additionally, we analyzed a real-world dataset on body fat to illustrate the practical relevance and effectiveness of our new estimator, showing significant reductions in the estimated mean squared error. As a result, the precision of the estimated parameters improves substantially, fulfilling one of the primary objectives for practitioners in this field.
Depression severity detection from facial expressions in videos using recurrent neural networks
Major Depressive Disorder (MDD), commonly known as depression, impacts over 300 million people worldwide. Diagnosing this condition often relies on subjective judgment, emphasizing the need for an objective approach. Deep learning, particularly Recurrent Neural Networks (RNNs), offers a promising solution, especially for analyzing multivariate time series data. Researchers have explored the use of RNNs and their variants to detect depression severity. Therefore, this study conducts experimental testing to identify depression severity using first derivative techniques and feature engineering on the RNN model and its variations. The first derivative is calculated for each frame during the subject’s interview, and feature engineering techniques focus on the eyes and lips, known to be associated with depression, including calculations of upper and lower lip distances, eye openness, and more. The RNN model, incorporating feature engineering, achieved the best results among the proposed methods, with a Mean Absolute Error (MAE) of 5.04 and Root Mean Squared Error (RMSE) of 6.03. However, further performance enhancement is possible by increasing the number of layers and neurons, considering the current model’s relative simplicity due to limited resources.
Mathematical modeling of human–rodent monkeypox infectious disease using a hierarchical approach
Monkeypox is a resurging zoonotic disease in Nigeria, posing increasing public health concerns. To capture its transmission dynamics, this study develops a hierarchical human–rodent model. Biological validity is ensured by proving the positivity of solutions and identifying an invariant region. Epidemic threshold analysis is conducted through the derivation of the disease-free equilibrium (DFE). The model combines theoretical analysis and numerical simulation in a hierarchical framework. Using the adaptive fourth–fifth order Runge–Kutta method (RK45), the nonlinear system is solved to investigate epidemic trajectories in Nigeria under realistic demographic and epidemiological settings. Results highlight the sensitivity of epidemic waves to transmission parameters and emphasize the role of rodent reservoirs in sustaining outbreaks. The study provides computational and analytical insights that may inform public health interventions to control monkeypox spread.
Lung cancer classification using vision transformer: a CRISP-DM approach with histopathological imaging
Lung cancer classification based on histopathological imaging plays a pivotal role in achieving early detection, accurate diagnosis, and effective treatment planning. Conventional diagnostic methods, including manual examination of histopathological slides and radiological imaging, are often subjective and time-consuming. Their limited ability to capture complex morphological patterns further constrains diagnostic accuracy. In response to these limitations, the present study employs the Cross-Industry Standard Process for Data Mining (CRISP-DM) framework to systematically evaluate the application of the Vision Transformer (ViT) in lung cancer classification. The LC25000 dataset, comprising three histopathological categories: adenocarcinoma, squamous cell carcinoma, and benign lung tissue. It was utilized for model evaluation. All images were resized to 224 × 224 pixels, and data augmentation techniques were applied to enhance generalization capability. The ViT model was implemented using TensorFlow and trained with the Adam optimizer (learning rate = 0.0001, batch size = 16, epochs = 50), employing early stopping and learning rate scheduling to mitigate overfitting. The proposed model achieved an overall accuracy of 0.97, with precision, recall, and F1-scores consistently exceeding 0.97. Class-level analysis demonstrated exceptional performance in identifying benign tissue (precision = 0.999, recall = 1.000, F1 = 0.999) and robust classification of malignant subtypes, including adenocarcinoma (F1 = 0.957) and squamous cell carcinoma (F1 = 0.959). These results emphasize the ViT’s strong capability in capturing global contextual features, surpassing conventional CNN-based methods that primarily rely on local feature extraction.
A compartmental modeling of crime influenced by drug consumption
This article proposes a discrete compartmental model to analyze the influence of drug consumption on crime dynamics and to assess the effectiveness of different intervention strategies. The population is divided into five categories: susceptible individuals, drug users, active criminals, prisoners, and rehabilitated individuals. Three control functions are introduced: rehabilitation of drug users, social reintegration of rehabilitated individuals, and awareness campaigns. Based on optimal control theory and Pontryagin’s maximum principle, the necessary conditions for identifying optimal strategies are established. Numerical simulations carried out using MATLAB complement the theoretical analysis and illustrate the behavior of the system with and without intervention.
Modeling and analysis of the food chain's dynamics incorporating flowers, pollinators, and predators: the role of odors
For ecological interactions and plant reproduction, scents play a critical part in the food chain, which includes flowers, pollinators, and predators. Floral volatiles are important cues that attract pollinators, which in turn help plants reproduce. Additionally, these smells can affect predators and other higher trophic levels, thereby altering the dynamics of a community. To comprehend how the odor affects their dynamics, this work suggests and examines a food chain model of the aforementioned kind. The food chain model's stability analysis is examined locally with the help of linearization techniques and globally utilizing suitable Lyapunov functions. The possibility of local bifurcations occurring is examined, along with determining their kind using the Sotomayor theorem for local bifurcations. To validate the acquired analytical results and comprehend the influence of parameter values, a numerical simulation is performed.
Impact of food intake on glucose and insulin regulation: an integrated mathematical model
This study presents a novel and original mathematical model that integrates glucose, insulin, beta cells, and food intake dynamics to explore their interrelationships and impact on glycemic regulation. The model incorporates differential equations representing the changes in glucose levels, insulin secretion, beta cell activity, and dietary intake. By analyzing the stability of equilibrium points, we aim to understand how variations in food intake influence glucose and insulin dynamics. The originality of this model lies in its comprehensive approach to incorporating food intake as a critical factor in glucose homeostasis. The results provide insights into the mechanisms governing glycemic regulation, offering a framework for predicting the effects of dietary changes and improving diabetes management strategies. This model has potential applications in clinical settings, aiding in the personalization of dietary recommendations and therapeutic interventions for individuals with diabetes.
Optimal control strategy and validation of the SVITR model for influenza A (H1N1) virus
In this work, a SVITR compartmental model is developed for representing the spread of Influenza A (H1N1) and a 3-variable control strategy is developed comprises of vaccination, treatment and awareness program. The real-world data for Influenza A (H1N1) is considered from the state of West Bengal during 2019-2024 as reported by National Centre for Disease Control (NCDC). Model is compared with the collected data and significant comparative trajectory is found year wise. The control strategy is developed using Pontryagin’s minimum principle. The impact of different parameters is based on normalized sensitivity analysis method. Positivity and boundedness of the model is found. Also, stability analysis was performed corresponding to equilibrium points, and it is observed that the model shows stability when Basic Reproduction Number R0 < 1, which is also reflected in the collected data.