Complexity Analysis Of Several Kinds Of Stochastic SIS Epidemic Model

In recent years,with environmental pollution,ecological destruction and frequent population flow,epidemic diseases have serious effects on human health and life safety.Therefore,the epidemic diseases has made the research particularly important on its pathogenesis,regularity of epidemic and control strategy.Epidemic dynamics is an important method of theoretical research on infectious diseases.By establishing mathematical models to study the epidemic diseases,it reflects regularity of epidemic in respect of transmission mechanism to give a view on the overall pattern of disease prevalence.Considering the influence of random factors on the transmission of infectious diseases,this article establishes some stochastic model of infectious disease by adding random disturbance to a deterministic epidemic model.This paper is divided into five chapters.In the first chapter,we briefly introduce the background of epidemic,dynamic epidemic development,research results and main content of this paper.In the second chapter,we establish the dynamics of a stochastic SIS epidemic model with saturated incidence and double noises.The stochastic SIS epidemic model is simplified to Ito equation by stochastic averaging method.And we analyze the existence of the disease free equilibrium and the endemic equilibrium.By dint of the Lyapunov exponent of invariant measure and the stationary probability density,the stochastic bifurcation of the model was explored and.It is analyzed that the location and probability which the stochastic system occurred stochastic Hopf bifurcation under the different parameters.In the third chapter,the epidemic model of incubation period and recovery period has been discussed.We address the effect of stochastic perturbation on a nonlinear double delays SIS epidemic model.By the Lyapunov functional method,we discuss the stability of the system around the endemic equilibrium state.We obtain the sufficient conditions for model parameters,It is the asymptotical mean square stability and stability in probability for time delays around the equilibrium.Finally,the Euler-Maruyama approximation method is performed to illustrate our theory.In the fourth chapter,the dynamics of a stochastic SIS epidemic model with Levy jumps and saturated incidence is investigated.The existence of the global positive solution is first obtained.Then,the conditions of the persistence and the extinction of the model were obtained by making use Lyapunoy function,Ito formular and martingale theory etc.Finally,according to R0,we discuss that asymptotic behavior of disease equilibrium.In the fifth chapter,we briefly review the previous conclusions and the research content of practical biology significance.Finally,we analyzed some of the deficiencies and problems need to be further study and work.