Dynamics Study On Several Kinds Of Stochastic Epidemic Models

Outbreaks of infectious diseases have caused substantial deaths,social and economic losses in the whole world.It is of great significance to study the dynamics of diseases.Mathematical modeling has become an important and powerful tool that helps understand the transmission and control of diseases.Many studies of mathematical epidemiology assume that model parameters are precisely known.However,they can be imprecise due to various uncertainties and unknown data.Environmental perturbations and information intervention strategies can also influence the spread of diseases.Therefore,this paper introduces environmental noises,interval parameters and information intervention strategies into the epidemic models to study their dynamic behavior.The details are as follows:(i)A stochastic SIRS epidemic model that includes interval parameters and white noises is studied.We define the stochastic basic reproduction number,when it is less than one,the disease is predicted to die out with probability one.When it is greater than one,the model admits a stationary distribution.Thus,larger stochastic noises(resulting in a smaller stochastic basic reproduction number)are able to suppress the emergence of disease outbreaks.Using numerical simulations,we also investigate the influence of parameter imprecision on the epidemic system.These parameters can greatly affect the long-term behavior of the system.(ii)We study the dynamics of an imprecise SIRS epidemic model with Levy jumps.We prove that the model has a unique global positive solution.Sufficient conditions for persistence and extinction of the disease are obtained.Numerical simulations are carried out to show the in-fluence of sudden environmental perturbation on disease dynamics.These results suggest that Levy noise can greatly affect the dynamics of the epidemic system.(iii)The dynamics of a stochastic hepatitis B virus(HBV)infection model with intervention strate-gies is analyzed.By using the Markov semigroups theory,we find that a threshold can be used to govern HBV.Numerical simulations are also carried out to investigate the influence of infor-mation intervention strategies that may change individual behavior and protect the susceptible from infection.Our analysis shows that the environmental noise can greatly affect the long-term behavior of the system,highlighting the role of intervention strategies on the control of HBV.