Stability And Hopf Branches Of Several Infectious Disease Models With Time Delay

Infectious diseases pose a huge threat to people's lives,in order to reveal the epidemic law of infectious diseases and predict the development trend,we have carried out some studies on the dynamic behavior and the existence and properties of infectious disease models,This paper is divided into five parts.In chapter 1,we briefly introduce the background and research status of epidemic,and the stability of DDE,Hopf bifurcation-related theories,central manifolds,and Normative theory.In chapter 2,we consider a class of infectious disease models with time delay and nonlinear infection rate,obtain the basic regeneration number of the model On the basis of the existence of time delay,and the condition of branch existence,analyse the stability of the equilibrium point,and verify the result by numerical simulation.In chapter 3,on the basis of an infectious disease model with public education,time delay is introduced to simulate the incubation period,disease based on this basis,analyzes the stability of equilibria systems,as well as of Hopf branch,at the same time,using the theory of center flow and specifications to determine the direction and Hopf branch is given the periodic solution and the specific expression of cycle stability,and gives examples to carry on the numerical simulation verifies the correctness of the conclusion.In chapter 4,we consider the influence of public education on disease transmission,a kind of infectious disease model is established,the basic regeneration number of the model is calculated,the stability of the equilibrium point of the model is analyzed,the conditions of branch existence are obtained,and the correctness of the conclusion is verified by numerical simulation.In chapter 5,conclusions and Perspectives.Summarized the work of this paper,and prospecte the future research direction.