Abstract:

In this paper, we study an HIV infection model with saturation incidence rate, CTL immune response, immune impairment, and intracellular delay. Firstly, the basic reproduction ratio $ \Re_{0} $ of virus infection is obtained by using the next generation matrix method. Secondly, the local stability of feasible equilibria is proved by analyzing the distribution of the root of the corresponding characteristic equations. By constructing appropriate Lyapunov functionals and using LaSalle's invariance principle, we prove that when $ \Re_{0}<1 $, the virus infection-free equilibrium is globally asymptotically stable; when $ \Re_ {0}>1 $, the immunity-inactivated equilibrium is globally asymptotically stable. Finally, the parameter with critical influence on $ \Re_{0} $ is determined by the parameter sensitivity analysis.

Key words: HIV infection, Intracellular delay, CTL immune response, Immune impairment, Stability analysis