Stability of an HIVAIDS Treatment Model with Different Stages

Abstract EN

An HIV/AIDS treatment model with different stages is proposed in this paper.

The stage of the HIV infection is divided into two stages, that is, HIV-positive in the asymptomatic stage of HIV infection and HIV-positive individuals in the pre-AIDS stage.

The fact that some individuals with HIV-positive individuals after the treatment can be transformed into the compartment of HIV-positive individuals in the asymptomatic stage of HIV infection, the compartment of HIV-positive individuals in the pre-AIDS stage, or the compartment of individuals with full-blown AIDS is also considered.

Mathematical analyses establish the idea that the global dynamics of the HIV/AIDS model are determined by the basic reproduction number R0.

The disease-free equilibrium is globally asymptotically stable if R0<1.

The endemic equilibrium is globally asymptotically stable if R0>1 for a special case.

Numerical simulations are also conducted to support the analytic results.