Dynamic Analysis For Several Kinds Of Stochastic Epidemic Models With Lévy Noise

For thousands of years,infectious diseases have seriously threatened human health and hindered the development of society.Therefore,mankind began to use mathematical methods to study the transmission law of infectious diseases,find methods to control the transmission of infectious diseases,and have achieved many excellent results.The outbreak of COVID-19 at the end of 2019 has had a great negative impact on human production and life,and is still spreading all over the world.It makes the study of the transmission law of infectious diseases and the exploration of methods to control the spread of diseases become one of the hot topics in the world again.Due to the randomness of real conditions,infectious disease systems may suffer from sudden environmental interference such as earthquakes and mountain torrents.The continuous stochastic model can not describe this,so Lévy noise needs to be introduced to describe the sudden environmental interference.This paper mainly studies the dynamic behavior for several kinds of stochastic epidemic models with Lévy noise,which are: stochastic SEI epidemic model with Lévy noise,stochastic SIQS epidemic model with Lévy noise and Markovian switching as well as stochastic SIS double disease model with Lévy noise and different incidence.The main work is as follows:Chapter 1 and chapter 2 introduce the research background,the current research situation at home and abroad,the structure of the whole article and some preliminary knowledge involved in this paper.In chapter 3,a stochastic SEI epidemic model with Lévy noise is studied.It is proved that the solution of the model is a global positive solution,the stochastically ultimate bounded is discussed by the basic inequality and Chebyshev inequality,the asymptotic behavior around the two equilibrium points is discussed,and the sufficient condition for extinction and persistence of infectious diseases are given.In chapter 4,a stochastic SIQS epidemic model with Lévy noise and Markovian switching is investigated.The existence of a unique global positive solution of the model is proved,and the sufficient conditions for the extinction and persistence of infectious diseases are obtained by using the knowledge of stochastic analysis,and in the case of persistence,the sufficient conditions for the existence of positive recurrence of the solution is given.In chapter 5,the dynamics analysis of a stochastic SIS epidemic model with different incidence and double diseases driven by Lévy noise is studied.By using Lyapunov function and It?o formula,the existence of global positive solution of the model is discussed,the conditions of extinction and persistence of double diseases under the influence of white noise and Lévy noise are shown,furthermore,we explore the condition under which the two diseases coexist.