Dynamical Analysis Of HIV Models With Latent Infected Cells And Immune Response

In this paper, HIV Models with latent infected cells and immune response are studied. By constructing Lyapunov functions, we analyze the global dynamics of these models. There are five chapters.In the first chapter, we introduce the related knowledge of HIV and the antiviral immune response as well as some basic stability results of theory which will be used in this paper.In the second chapter, we study an HIV dynamic model with latent infected cells and self-regulating immune response, analyze its local and global dynamical behaviors, and propose suf-ficient conditions for equilibria to be globally stable.In the third chapter, we further study the impact of the stimulating immune response to HIV infection. We prove local stability and global stability of the disease-free equilibrium and the in-fective equilibrium by using Routh-Hurwitz criterion and Lyapunov-Lassale invariance principle, respectively.In the fourth chapter, on the basis of the previous two chapters, we further study an HIV dynamic model with latent infected cells and a more general immune response. We consider the impact of the self-regulating immune response and the stimulating immune response to the dynamical behaviors, then analyze the global dynamical behaviors of the system by using Lyapunov-Lassale invariance principle.In the fifth chapter, we summarizes the main conclusions of this paper and present the corresponding biological explanations as well as some points for further research.