Stability Analysis Of Two Classes Of Epidemic Models

In this paper,we mainly build and study the dynamics of two classes of infectious disease systems.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,an SIRS epidemic model with the impact,of media coverage is proposed and analyzed.The basic reproductive number R0 and the existence of the equilibria are obtained.If R0<R0*<1,the disease free equilibrium is globally asymptotically stable by constructing Lyapunov function.Furtbermore,The existence of an optimal control is proven,and an explicit expression for optimal control is obtained.In Chapter 3,we studied a model of fractional HIV-1 infection with time delay and Logistic growth.First.the corresponding fractional order model is established on the basis of the integer order HIV-1 model.Secondly.the boundary of the solution and the existence of the equilibrium are proved.Then,we get the threshold parameter of the model and analysis the stability of the disease free equilibrium and the endemic equilibrium,and gives the time-delay balance keep asymptotically stable under some condition and the existence condition of the Hopf branch.