Dynamics Analysis Of Some Classes Stochastic Epidemic Models

Infectious diseases caused by viral infection have aroused great attention from all over the world to public health.However,in the real world,the environment in which the population is located is variable and inevitably disturbed by environmental noise,the environmental noise will affect many parameters of the system.Therefore,in order to better study and predict the spread of infectious diseases,the use of stochastic model will be more in line with the actual biological significance.In this paper,three classes of stochastic epidemic models are presented and investigated.The whole 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,we propose and study a class of stochastic HIDV epidemic model of hepatitis B infection disease with time delay and intracellular HBV DNA-containing capsids.First,we prove that the stochastic system exists a unique global positive solution.Then,by establishing appropriate Lyapunov functional,as well as applying Ito formula and some important inequal-ities,we obtain the sufficient conditions that the solution of the stochastic system fluctuates around the disease-free equilibrium and the positive equilibrium of the deterministic model.In the end,numerical simulations are implemented to verify our analytical results,this also show that stochastic disturbance is conducive to the diseases of hepatitis B control.In Chapter 3,a class of stochastic SICR viral epidemic model is considered.First,using Lyapunov function and Ito formula,we prove that the stochastic system exists a unique global positive solution.Then,by means of the theory of Hasminskii,we get that the stochastic system has a unique stationary distribution,this signifies that the disease is persistent.Furthermore,we attain the sufficient conditions for the extinction and persistence of the disease with the help of the method of Strong law of large number.Finally,we will proceed in a numerical simulation to justify the theoretical results.In Chapter 4,we set up and discuss a class of stochastic rumor spreading model with the different attitudes towards rumors.By the similar method used in Chapter 3,we apply the theory of stochastic differential equation to carry on a comprehensive study for the model established in this chapter,we first prove the existence of the globally unique positive solution of the stochastic model.Then,we analyze the existence of the stationary distribution of the stochastic system.Furthermore,sufficient conditions for the extinction and persistence in the sense of the rumors are obtained.Eventually,numerical simulations are carried out in order to verify our analytical results.In Chapter 5,the main work of this paper is summarized and the future research work is prospected.