Dynamic Behaviors Of Two Classes Of Stochastic SVIR Epidemic Models With Vaccination

The spread of epidemic has brought great harm to human health and social stabil-ity.Epidemiological dynamics method is one of the most important methods to study the characteristics of epidemic transmission,it has important theoretical and practical value in the prevention and control of epidemic transmission.Epidemiological dynamics method establishes an epidemic dynamic model which can describe the characteristics of epidemic transmission more accurately,and uses various mathematical theories and methods to study the dynamic behavior of the model,so as to provide a theoretical basis for preventing and controlling the occurrence and spread of epidemics.Vaccination is an important measure to prevent and control the spread of epi-demics.Meanwhile,we should consider the random and unpredictable variation of the environment.Therefore,two classes of stochastic SVIR epidemic model with vaccina-tion are established in this paper,the dynamic behavior of the system is studied by stochastic differential equation theory.This paper is divided into the following four chapters:In chapter one,we introduce the background and significance of the epidemic model,and give some basic definitions and preliminaries of the paper.In chapter two,we study the dynamical behavior of SVIR model with nonlinear in-fection rate.Firstly,we discuss the existence,uniqueness and global positive of solution and analyze the extinction and permanence of the disease.Further,the conditions of the stationary distribution of the stochastic system are given,and the existence of the nontrivial periodic solution of the periodic stochastic SVIR model is proved.Finally,numerical simulations validate the analytical results.In chapter three,we analyze the dynamical behavior of SVIR model with high order stochastic perturbation.By constructing an appropriate Lyapunov function,the existence of the global positive solution of the model is discussed,and the conditions of the stationary distribution of the stochastic system are analyzed.Furthermore,the existence of nontrivial periodic solutions to SVIR model with periodic coefficients is proved.Finally,numerical simulations validate the analytical resultsIn chapter four,we summary our works,point out the shortcomings,and make a prospect for the future work.