Research Of An Infectious Diseases Ecological Mode With Time Delay And Pulse

This paper studied two kinds of ecological infectious diseases models the one with time delay and the other one with pulse vaccination, the stability of the models were studied respectively too, and has acquired some achievements. The paper mainly divided into four parts.The development history of ecological infectious diseases, current work background, the direction and valuable significance of ecological infectious disease research were summarized in the first part of the paper, and in this part we also introduced the work of the paper.In Chapter 2 we discussed some problems of the ecological infectious diseases model with time delay. Firstly, we got the condition of the existence of positive equilibrium point global stability and the Hopf bifurcation in such system. Then the direction of Hopf bifurcation of the system and the condition of periodic stable were studied though the method in literature [2].In the third part we had a research on the disease-free periodic solution of the ecological infectious diseases models with pulse vaccination, and obtained its sufficient condition of disease-free equilibrium point.The last part of the paper had an summarize of the previous paper, and prospected the author later research direction and the future of ecological epidemiology.