Dvnamical Behaviors Of Two Classes Of Infectious Disease Models

In this paper, we mainly study the dynamics of two classes of infectious disease models. 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.In Chapter 2. the dynamics of a HCV virus transmission model is explored. Two thresholds of basic reproduction number and control reproduction number are derived. The sufficient con-ditions for the existence of infection-free equilibrium and endemic equilibrium are obtained. The globally asymptotical stability of equilibria are verified by constructing the Lyapunov functions. Numerical simulations are presented to support and complement the theoretical findings.In Chapter 3. a H7N9 avian-human influenza. model coupling within-host and between-host dynamics is studied. new reproductive numbers for both the isolated systems and the coupled system are derived. The eigenvalue method and Routh-Hurwitz criterion is applied to analyze the stability of equilibria. And we also get that the stability of the equilibria of the fast and siow systems are connected to the new reproduction numbers. Finally, numerical simulations are presented to explain the mathematical conclusions.