The Stability Analysis Of Some HIV Infection Models With Immune Response

In recent decades, more and more scholars began to study the pathogenesis of HIV from a micro perspective, a large number of models have been proposed. It is necessary to consider the immune system during the study of HIV models. The immune system is an important institution which can resist organic matter invade our body, and the immune system can identify "self" and "non-self".The first part is the introduction, we introduce some background, purpose and mean-ing of HIV immune models. The second part give some preliminaries. The third part, we study three different mathematical models to illustrate the positive effects of immune to prevent the HIV disease. The main content of the models can be summarized as follows:The first model, we investigate the global stability of HIV model with Beddington-DeAngelis incidence and humoral immune response. The model include an eclipse stage of infected cells, in this stage, the infected cells may revert to the uninfected class. We derive the basic reproduction number and the immune response reproduction number. By constructing suitable Lyapunov functionals, we prove the global asymptotic stability of the equilibrium. Finally, we check the stability about equilibrium with numerical simulations.The second model, we investigate the HIV model with humoral immune response and two delays. We discussed the local and global stability about the disease-free equilibrium, and the local stability about immune-free equilibrium and immune equilibrium. Finally, we discussed the effects of delays in the model, and we check our main results with numerical simulations.The third model, on the basis of the first two models, we investigate the dynami-cal behavior of delayed HIV model with humoral immune and CTL immune response. Our model describes the interaction of HIV with two target cells:CD4+T cells and macrophages. By constructing suitable Lyapunov functionals and using the LaSalle in-variance principle, we have shown that the equilibriums are globally asymptotically stable. Finally, we give some references which related to the paper.