Numerical Approaches to HIV/AIDS Dynamics: A SIAT Model Study

Abstract

In this study, we develop and analyze a nonlinear  model to investigate the transmission dynamics of HIV/AIDS with an emphasis on the role of treatment. The total population is stratified into four compartments: Susceptible (S), Infected (I), individuals with AIDS (A) and Treated (T). The model’s equilibriums are derived, and the basic reproduction number  is calculated as the threshold parameter governing disease persistence or eradication. Both local and global stability conditions of the equilibriums are rigorously established. A sensitivity analysis of  identifies the parameters most influential in driving HIV/AIDS progression, providing valuable insights for potential intervention strategies. To complement the theoretical analysis, three numerical schemes—Euler’s method, the fourth-order Runge–Kutta method, and the forward difference method—are employed to simulate system dynamics. A comparative evaluation highlights their relative accuracy and efficiency in capturing the model’s behavior. Numerical experiments, conducted using MATLAB, illustrate the impact of treatment and validate the analytical results.