Stability And Hopf Bifurcation Of The Epidemic Model With Cannibalism

In this paper,the stability and Hopf bifurcation of an epidemic model with cannibalism are studied.The main research content is divided into three chapters.In chapter 1,the research background and research status of the biological cannibalism behavior and infectious disease model with the cannibalism behavior is introduced.In chapter 2,a epidemic infectious disease model with cannibalism is discussed.The boundedness of the model is studied,the existence of the positive equilibrium point of the model is discussed,and the conditions for the local asymptotic stability of the positive equilibrium point are given.The Liapunov function is constructed and the global stability of the system is analyzed by Bendison's theorem.In chapter 3,a model of epidemic diseases with time delay is discussed.Research on classification discussion method of two time delays in the system,two time delays is studied respectively in single-delay system and double-delay system,the parameter interval of Hopf bifurcation time-delay classification is discussed.Finally,the direction property of Hopf bifurcation is proved by the Central manifold theorem.