Study On Delayed SEIR And SIR Epidemic Models

Kermack and McKendrick established the compartment model and threshold theo-rem. In almost all infectious diseases model of this field, the researchers focus on one important parameter which is the basic reproduction number R0. It plays an important role in the whole research field of epidemic. In order to prevent the epidemic, we have to find R0, and calculate the parameters that have effect on R0. By controlling the parameters,we can achieve the purpose of controlling disease. The main content of this paper is organized as follows:In Chapter 1, the basic theory of infectious disease model is outlined,including the historical background, the significance of the epidemic dynamics and the epidemic model on heterogeneous networks.In Chapter 2, by introducing the birth pulse, pulse vaccination, horizontal, vertical transmission and transmission delay into the SEIR epidemic model, we can obtain a small range of R0.We mainly apply the comparison theorem of the impulsive differential equations.In Chapter 3, nonlinear analysis of SIR epidemic model for heterogeneous network is studied. By using the comparison theorem and iterative principle, the solutions of (3.1.1) system and global behavior are obtained, then we get the threshold conditions of the reproduction number whether the disease spreads.