Analysis Of Dynamic Of Stochastic SIRI Epidemic Models With Nonlinear Incidencey

The spread of infectious diseases will hinder the economic development of society.Although humans have achieved some results in eliminating and controlling certain diseases,with the destruction of the ecological balance and the resistance of the human body to drugs,the prevention and control problems are becoming increasingly prominent,especially the epidemic caused by the new coronavirus outbreak in Wuhan,China in 2019,which poses a serious threat to the lives and economy of people in China and the world.Therefore,it is even more important to study the spread of infectious diseases and find ways to control the spread of diseases.There are many kinds of epidemic models.This paper mainly studies the dynamic behavior of the system when the contact rate of the stochastic SIRI epidemic model with nonlinear incidence is interfered by white noise,and considers the existence of periodic solution and ergodic stationary distribution of the stochastic system with Markov regime switching and the parameter is T-periodic function.The main work is as follows:Chapter 1 and chapter 2 mainly introduce the research background,the current research situation at home and abroad,the layout of the whole article and some preliminary knowledge needed in this paper.In chapter 3,based on the important role of incidence in the spread of disease,the dynamic behavior of contact coefficient of stochastic SIRI epidemic model with nonlinear incidence is studied when it is disturbed by white noise.By constructing appropriate Lyapunov function,using It?o formula,martingale's strong large number theorem and other related stochastic differential equation theory,the existence and uniqueness of global positive solution of the system is proved.The asymptotic behavior of stochastic systems near the disease-free equilibrium and local equilibrium of deterministic systems,and the results are verified by numerical simulation.In chapter 4,we establish a stochastic SIRI epidemic model with the incidence of Beddington-DeAngelis and the contact rate disturbed by white noise,and its coefficient is a T-periodic function,and prove the existence and uniqueness of the global positive solution of the system.The existence of periodic solution of the system is proved by using Has' minskii's theory,and the condition of disease extinction is studied at the same time.In chapter 5,a stochastic SIRI epidemic model with Markov regime switching is established,the existence of ergodic stationary distribution and the sufficient conditions for disease extinction are studied,and the correctness of the conclusion is verified by numerical simulation.