Dynamics Of HIV Infection Model With Delay Immune Response

In this paper, several HIV infection models with CTL-immune response are discussed and the dynamic behaviors of those models are analyzed. Based on the fact that a latent period between antigenic stimulation and generating CTLs, constant delay is introduced in the systems.This paper is composed of three chapters.In the first chapter, the history, background of dynamics of HIV infection models are briefly reviewed. Furthermore, we simply introduced the main work in this paper.In the second chapter, a model for HIV infection with delay in immune response is considered. The global stability of the infection-free equilibrium is analyzed, and the sufficient conditions of local stability of the CTL-absent infection equilibrium and CTL-present infection equilibrium are obtained. Numerical results show that if production rate of uninfected cells is large so that the basic reproductive ratio satisfies the existing condition of CTL-present infection equilibrium and it is below a certain threshold, the delay has no effect to the stability of the equilibrium; but if the basic reproductive ratio is greater than the certain threshold, and delay in immune response increases, the stability switches occur and equilibrium is unstable; moreover, a series of Hopf bifurcations and periodic solutions are observed.In the third chapter, a improved model based on the model of chapter 2 is considered because the production CTLs also depends on the population of CD4+T cells. The global stability of the infection-free equilibrium is analyzed and sufficient conditions for the local stability of the CTL-absent equilibrium and interior equilibrium are given. By choosing the CTL-response delayτas a bifurcation parameter, we prove that the interior equilibrium is locally asymptotically stable in a range of the delay and Hopf bifurcation occurs asτcrosses a critical value. Numerical simulations are given to support the theoretical results.