Solving SIR Model of HIV Using Implicit Multistep Method of Order Four and Dormand-Prince Method

Abstract

This study explored numerical methods to solve the SIR model for HIV dynamics, focusing on the implicit multistep method of order four and the Dormand-Prince method. These methods are applied to understand and predict the spread of HIV, evaluating their accuracy using different step sizes. Through computational simulations using MATLAB software, comparisons were made between the two methods at step sizes of h = 0.01 and h = 0.1. Results indicated that the Dormand-Prince method, especially at a step size of h = 0.01, provided more accurate predictions of HIV cases compared to the implicit multistep method of order four. The smallest step sizes enhanced accuracy and reduced errors, underscoring the importance of method selection and step size in HIV case predictions. The Dormand-Prince method, particularly at the smallest step sizes, emerged as a promising tool for accurate HIV modeling, aiding in understanding disease dynamics and informing public health strategies.