Study On A Class Of Stochastic SIRS Epidemic Model With Standard Incidence And Information Intervention

When an epidemic breaks out,it takes a long time to develop a vaccine,so information intervention is very important at this time.Besides,noise and time delay also have a certain impact on epidemics.This paper combines Lahrouz's model with Kumar's model and uses the standard incidence rate to form the studied model.The properties of the models with white noise,Levy noise and time delay respectively are analyzed.The details are as follows:(1)The properties of stochastic SIRS epidemic model with standard incidence and infor-mation intervention are studied.A stochastic model with white noise is established.A stopping time is defined.Then the existence of a unique global positive solution is proved by constructing a suitable Lyapunov function to prove the stopping time is infi-nite.The stationary distribution and ergodicity of the model is showed by constructing a compact set and appropriate Lyapunov function.It is also proved that the extinction of the disease.(2)The properties of SIRS epidemic model with standard incidence and information in-tervention driven by Levy noise are studied.A model with Levy noise is established.A stopping time is defined.Then the existence of a unique global positive solution is proved by constructing a suitable Lyapunov function to prove the stopping time is infi-nite.In addition,the asymptotic behaviors of model's solution around the disease-free equilibrium point and the endemic equilibrium point of its corresponding deterministic model are studied by constructing suitable Lyapunov functions respectively.(3)The properties of time-delay SIRS infectious disease model with standard incidence and information intervention are studied.A time-delay deterministic model is estab-lished.Local asymptotic stabilities and global asymptotic stabilities of disease-free equilibrium point and endemic equilibrium point are discussed.A stochastic model with time-delay is established.The existence of a unique global positive solution and the asymptotic behaviors of model's solution around the disease-free equilibrium point and the endemic equilibrium point of its corresponding time-delay deterministic model are studied.