Dynamic Behaviors Of Multi-group Stochastically SIQS Epidemic Model

With the rapid development of modern society,the environmental pollution is more and more serious,and the communication and contact between people become frequent and close.All of these lead to the increasing types and quantities of infectious diseases.The infectious disease has a fatal impact on our health and life.Therefore,it has a high theoretical significance and applicable value to research of infectious diseases.We usually establish the mathematical model when we research the evolution of infectious disease.We may obtain the dynamical behaviors of such a model by using mathematical theory and mathematical methods.In this paper,we mainly discuss the multi-group stochastic SIQS epidemic models.With the theory of stochastic differential equations,we analyze the dynamic behaviors of the system,which provide a theoretical basis for controlling the spread of infectious diseases.The paper is divided into four chapters.In chapter one,we introduce the background and significance of multi-group s-tochastically SIQS epidemic models and give some required knowledge.In chapter two,we discuss the stochastic SIQS epidemic model.For the deter-ministic SIQS epidemic model,we prove the existence and uniqueness of the endemic equilibrium,and obtain the globally asymptotical stability of the endemic equilibrium under the certain conditions.Then,we introduce the stochastic SIQS epidemic model,and prove the stochastic asymptotical stability of the endemic equilibrium.In chapter three,we consider multi-group stochastically SIQS epidemic model.Firstly,we discuss the positivity and boundedness of the solution of deterministic multi-group SIQS model,and analyze the global asymptotically stability of the free-disease equilibrium and the existence of endemic equilibrium.Then,we introduce the random perturbation,and establish the multi-group SIQS model with random perturbation.By using the theorem of Lyapunov asymptotically stability and Ito’s formula,the global stochastically asymptotically stability of endemic equilibrium of the model is proved.In chapter four,we make a conclusion for this paper,and point out the shortcom-ings of the paper and next work in the future.