| Epidemic dynamics is an important method of theoretical research on infectious dis-eases. It reflects regularity of epidemic in respect of transmission mechanism by math-ematical modeling to give a view on the overall pattern of disease prevalence. In this paper, we mainly study epidemic models with nonlinear incidence rates and time delays. This paper is divided into four chapters.In the first chapter, we briefly introduce the background of epidemic, research results and some basic theories of epidemic dynamics.In the second chapter, we establish an SIR epidemic model with incubation time delay and general nonlinear incidence rate. We analyze the existence of the disease free equilibrium and the endemic equilibrium of the full-system. We also study the conditions for the local or global stability of each equilibrium, and prove the stability of the system.In the third chapter, we establish an SIR epidemic model with recover time and general nonlinear incidence rate. We analyze the existence of the disease free equilibrium and the endemic equilibrium of the full-system. We also study the conditions for the local or global stability of each equilibrium, and prove the stability of the system.In the last chapter, we make a brief review of the above conclusions, and present the epidemiological and practical meaning for these models. And we analyze some short-comings of this paper and point out some questions and future work. |
