Stability Analysis Of Two HIV Infection Models

In this paper, based on the two kinds of saturation incidence proposed by Song and Neu-mann、Bairagi and Adak, we develop two HTV infection models considering the self-regulating CTL immune response and an infection time delay, respectively. The dynamic properties with their biological meanings are studied.Background knowledge about HIV, evolution of viral dynamics, advances of the saturation incidence and some basic theory are introduced in Chapter 1.In Chapter 2, an HTV infection model is studied, which incorporates the self-regulating CTL immune response and the saturation incidence, proposed by Song and Neumann. We study the global stability analysis of this model. By the help of the Hurwitz criterion and Lyapunov functions, it is shown that the global stability of the model is totally determined by the virus reproductive numbers. When Ro < 1, the infection-free steady state is globally asymptotically stable; when Ro > 1, the endemic equilibrium is globally asymptotically stable.In Chapter 3, an HIV dynamic model with the saturation incidence, proposed by Bairagi and Adak, and an infection time delay is proposed. We also present the global stability analysis of this model. We introduce the basic reproductive numbers for viral infection and CTL immune response, and we show that the global stability of the model is totally determined by this two basic reproductive numbers. By the help of the proving method for theorem 3.1 and theorem 3.2 in reference documentation [13], and via constructing Lyapunov functions, we obtain that: when Ro < 1, the system has an infection-free steady state, and it is globally asymptotically stable; when Rc < 1< Ro, the the system has an immune-free infection equilibrium and it is globally asymptotically stable, too; when Rc > 1, the system has an endemic equilibrium and it is globally asymptotically stable.