Modeling and analysis of an SIQRC system with fractional differential equations, cross-immunity, and inhibitory effects

Abstract

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.