Threshold Dynamics In A Stochastic SIR Infectious Disease Model

In this paper,we use the theory of stochastic analysis,Ito formula,Khasminskii formula of stability theory to analyse the threshold dynamics of two stochastic SIR epidemic models.The content of the full text is divided into four chapters.The first chapter briefly describes the research background and research status,and finally simply describes the main work of this paper.The second chapter briefly introduces the relevant preliminaries.In chapter 3,we study the threshold dynamics of a class of stochastic SIR infectious disease model.Under appropriate conditions,the existence and uniqueness of globally positive solutions,the existence of stationary distributions and the extinction of diseases are studied respectively.The main research method is by constructing Lyapunov functions and by using qualitative analysis methods to overcome the difficulty that f(N)has no specific expression.In chapter 4,the threshold dynamics of a stochastic SIR infectious disease model are studied by using similar methods.Under appropriate conditions,the existence and uniqueness of globally positive solutions,the existence of stationary distributions and the extinction of diseases are proved by constructing Lyapunov function.The main difficulty is that we consider a more general contact rate function.Finally,numerical simulations are performed to confirm theoretical results.