Dynamics Of A Stochastic Epidemic Model With Vaccination And Nonlinear Incidence Under Regime Switching

In our daily life,humans are often infected with infectious diseases.Therefore,our research on the law of transmission of diseases helps to improve human control of the spread rate of infectious diseases.The initial study on the law of the spread of infectious diseases was established In the case of sexuality,but in actual life,there are a variety of uncertainties,so the study of the dynamic nature of the epidemic model under stochastic perturbation is more practically meaningful;this paper studies two types of transformation mechanisms.The dynamic nature of the stochastic epidemic model with non-linear incidence rate mainly analyzes the dynamic behavior of the stochastic epidemic model through some theories in stochastic differential equations and obtains some good conclusions.The main contents of this article are:In the first and second sections,the research background and current progress of the biomathematical model are introduced,and some definitions,lemmas,theorems,which used in the article are listed;In the third section,The first type of random infectious disease model studied in this paper is a stochastic SIVS model with nonlinear incidence and immunization immunity under the conversion mechanism.The expression of the model threshold R0S is defined and established appro-priate Liapunov functions and taken theoretical analysis such as Ito's formula,B-D-G inequality,Doob's inequality,B-C lemma,strong number theorem,etc.,to studied the ergodic steady state distribution of solutions for stochastic epidemic models,and the condition of threshold of disease extinction and persistent in probability are discrimina-tion.Finally,numerical simulations are build to prove the correctness of the conclusions.In Section IV,we mainly study the dynamic of nonlinear incidence ?f(S)g(I)stochastic SIRS epidemic model with the Markov chain and Levy jumps.Given the threshold ex-pression of the epidemic model and constructing the appropriate Liapunov function,use Ito's formulas and stochastic differential equations theories proves that the only solution to the disease solution is the existence of steady state distributions,the extinction of the disease and the persistence of the mean,furthermore,establishes corresponding numer-ical simulations.In section V,the results of this study are summarized and proposed several new problems to solve.