A dynamical model of pneumonia transmission in children under five years with nutritional factors

Abstract

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.