Analysis of a virus-resistant hiv-1 model with behavior change in non-progressors

Abstract

We develop a virus-resistant HIV-1 mathematical model with behavior change in HIV1 resistant non-progressors which was analyzed for both partial and total abstinence cases. The model has both disease-free and endemic equilibrium points that are locally asymptotically stable depending on the value of the associated threshold quantities RT and R′T . In both cases, a nonlinear Goh–Volterra Lyapunov function was used to prove that the endemic equilibrium point is globally asymptotically stable for special case while the method of Castillo-Chavez was used to prove the global asymptotic stability of the disease-free equilibrium point. In both the analytic and numerical results, this study shows that in the context of resistance to HIV/AIDS, total abstinence can also play an important role in protection against this notorious infectious disease.