Analyzing Stability and Bifurcation in an HIV Model with Treatment Interventions

Abstract

This study presents a comprehensive mathematical model for HIV infection dynamics in the presence of treatment, focusing on stability  analyses. The model incorporates treatment interventions and explores their impact on disease progression, viral load dynamics, and  population-level outcomes. A stability analysis was conducted to investigate the existence and properties of equilibrium points, including  disease-free and endemic equilibria. Analysis shows that there is existence of disease-free whenever the threshold quantity R₀ is less  than unity i.e. R₀ >1 , and otherwise epidemic when  R₀ >1 . Utilizing mathematical techniques and computational simulations, we  explore the stability of these equilibrium points under varying conditions and treatment scenarios. Our findings elucidate the critical role  of treatment in mitigating HIV transmission, reducing viral replication, and preserving immune function. This research contributes  valuable insights into the dynamics of HIV infection and the efficacy of treatment interventions in controlling the spread of the virus.