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 behavioural change in HIV-1 resistant non-progressors. The model has?both disease-free and endemic equilibrium points that are proved to?be locally asymptotically stable depending on the value of the associated reproduction numbers. In both models, a non-linear 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.

Keywords

• resistance
• behavioural change
• partial & total abstinence
• goh-volterra lyapunov function.