Solving SIR Model of Yellow Fever Using Dormand-Prince and Euler Method

Abstract

This study investigated numerical methods for solving the SIR model, which represents susceptible (S), infectious (I), and recovery (R) populations, in the context of yellow fever dynamics. The aim of this study is to evaluate the effectiveness of two numerical methods, the Dormand-Prince method and the Euler method, in solving the SIR model of yellow fever. Through numerical simulations using MATLAB R2024b software, the study examines the dynamics of susceptible, infected, and recovered populations over time to gain insights into the spread and control of yellow fever. The research includes parameters in SIR for validation, and comparison to ensure better approximation of the numerical solutions. Comparisons were made between the Dormand-Prince and Euler methods at step sizes of h = 0.01 and h = 0.05, with results indicating that the Dormand-Prince method, especially at h = 0.01, provided better approximations of yellow fever dynamics compared to the Euler method. Smaller step sizes improved performance and reduced errors, emphasizing the critical role of method selection and step size in studying disease spread. By addressing these aspects, the study provides valuable insight into yellow fever dynamics, supports public health strategies, and contributes to yellow fever epidemiology through the application of mathematical modelling and numerical methods.