The Study Of Some Classes Of Epidemic Models With Nonlinear Incidence Rate And Distributed Time Delay

In this paper, we mainly study the dynamics of some classes of epidemic model between single population and multiple populations. The article includes three chapters.The preface is in chapter1, we introduce the research background of this article, the main task and some important preliminaries.The Chapter2:in Section1, an SIR epidemic model involving information-related vaccina-tion, non-linear incidence rate and the information variable is studied. We get a critical value (?)o. When (1-po)(?)o<1, the disease-free equilibrium is stable, on the contrary, if (1-po)(?)o>1, the disease-free equilibrium is unstable and an endemic equilibrium appears. We study the local asymptotical stability and global asymptotical stability by using the Routh-Hurwitz criterion and the geometric method due to Li and Muldowney, respectively. Numerical simulations are carried out to illustrate the main theoretical results.In Section2: Based on the Section1, we study the permanence, extinction and global attractivity for a nonautonomous SIR epidemic model with saturation incidence rate and limited medical resources. We establish some sufficient conditions on the permanence and extinction of the disease. By Liapunov functional method, we also obtain some sufficient conditions for global attractivity of this model. In the end, numerical simulations are carried out to illustrate the main theoretical results.In Chapter3: A new epidemic model is proposed. We study the permanence, extinction and global asymptotic stability for a nonautonomous malaria transmission model with distributed time delay. We establish some sufficient conditions on the permanence and extinction of the dis-ease by using inequality analytical techniques. By a Liapunov functional method, we also obtain some sufficient conditions for global asymptotic stability of this model. Numerical simulations are given to explain the main analytical findings.