| The extinction and persistence of three classes of stochastic epidemic models with different environmental noise interference in this thesis are studied.The dissertation is divided into five chapters:The preface is in Chapter 1.This chapter introduces the research background,the main work of this article,as well as the preliminary knowledge.In Chapter 2,the parameter perturbation under white noise interference is introduced,and a stochastic SIR epidemic model affected by disease consciousness is studied.Firstly,the stochastic system exists a unique global positive solution is proved by applying the stochastic differential equation theory.Secondly,in addition to constructing the proper Lyapunov function,Ito formula and the strong law of large numbers are also used to obtain the sufficient conditions for the extinction and persistence of diseases.Finally,the correctness of the theoretical results obtained in this chapter is verified by numerical simulation.In Chapter 3,a stochastic SAIQH epidemic model of COVID-19 is established by introducing the nonlinear incidence function and the interference of white noise.It is proved that the stochastic system has a unique global positive solution in this chapter,and the sufficient conditions for disease extinction and disease persistence are obtained.These results are verified by numerical simulation.In Chapter 4,the interference of Levy noise is introduced,and a class of stochastic SQIR epidemic model with Levy noise is established.Using stochastic differential equation theory,firstly the model has a globally unique positive solution is proved.Besides,the positive invariant set is discussed.Then by using stochastic Lyapunov function,It(?)’s formula and the strong law of large numbers,the sufficient conditions for the persistence and extinction of the disease are obtained.Finally,numerical simulation is carried out.In Chapter 5,the main work of this paper is summarized and the future research work is prospected. |
