Dynamics Study Of Some Classes Stochastic Epidemic Models

In this paper,three classes of stochastic epidemic models are proposed and investigated to reveal the epidemic regularity of diseases under the interference of environmental noise.This paper is divided into five chapters:The preface is in chapter 1,we introduce the research background and main task of this article,as well as some important preliminaries.In Chapter 2,a stochastic hepatitis B epidemic model is established.Firstly,we prove that the stochastic system exists a unique global positive solution by the stochastic differential equation theory.Secondly,constructing the proper Lyapunov function and using the theory of Khasminskii,we get that the stochastic system has a unique stationary distribution.Then,the strong law of large numbers was used to obtain the sufficient conditions for the extinction of diseases.Finally,we verify the theoretical results obtained in this chapter by numerical simulation.In Chapter 3,based on the epidemic model with free-living pathogens discussed by predecessors,we establish and discuss a class of stochastic SIRTP viral epidemic model by considering white noise interference.By the similar method used in Chapter 2,we study the existence of the stationary distribution for stochastic system and obtain the sufficient conditions for the persistence and extinction of the disease.Then,the existence of nontrivial positive periodic solutions to the stochastic SIRTP epidemic model in periodic environment is discussed.Finally,we give some numerical simulations to support the analytical results.In Chapter 4,on the basis of on the definitive hepatitis C epidemic model studied in the literature,considering another form of the environment noise and proposing a class of stochastic SICR epidemic model driven by Levy noise.By means of the theory of stochastic differential equation,we prove the model has a globally unique positive solution.using stochastic Lyapunov e function,It?'s formula and the strong law of large numbers to give the sufficient conditions for the persistence and extinction of the disease.In chapter 5,the main work of this paper is summarized and the future research work is prospected.