The Study Of Some Classes Of Epidemic Models With Self Cure And Saturated Immune Impairment

In this paper, we mainly study the dynamics of some classes of epidemic model Including drug epidemic model and viral infection model. The article includes three chapters.The preface is in chapter 1, we introduce the research background of this article, the main task and some important preliminaries.The Chapter 2:in Section 1, an SIVS epidemic model with saturated incidence rate is studied. The locally asymptotically stable of equilibria are verified by Routh-Hurwitz criterion and eigenvalue method. We also discuss the globally asymptotically stable of disease-free equi-librium and the persistence of the system. Moreover, the globally stable of endemic equilibrium is proved by the limit system. In addition, numerical simulations are presented to support and complement the theoretical findings.In Section 2, we study the persistence, extinction and the global attractive of a nonau-tonomous drug epidemic model with distributed delay. Firstly, we get some sufficient conditions about the persistence and the extinction of the disease by analyzing the inequality. Secondly, we obtain the sufficient conditions for the global attractive of the system through using Lya-punov functional method. Finally, numerical simulations are presented to illustrate the main theoretical findings.In Chapter 3:the stability and Hopf bifurcation of a delayed viral infection model with logistic growth and saturated immune impairment is studied. The sufficient conditions for local asymptotic stability of the infection-free equilibrium and no-mamune equilibrium are given. We also discuss the local stability of the positive equilibrium and the existence of Hopf bifurcation. Moreover, the direction and stability of Hopf bifurcation obtained by using the standard form theory and center manifold theorem. Finally, numerical simulations are carried to verify the theoretical conclusions.