Ningzhong Shi

Asymptotic behavior of global positive solution to a stochastic SIR model

In this paper, we explore a stochastic SIR model and show that this model has a unique global positive solution. Furthermore, we investigate the asymptotic behavior of this solution. Finally, numerical simulations are presented to illustrate our mathematical findings.

Brief paper: Dynamics of a multigroup SIR epidemic model with stochastic perturbation

In this paper, we introduce stochasticity into a multigroup SIR (susceptible, infective, and recovered) model. The stochasticity in the model is introduced by parameter perturbation, which is a standard technique in stochastic population modeling. In the deterministic models, the basic reproduction number R0 is a threshold which completely determines the persistence or extinction of the disease. We carry out a detailed analysis on the asymptotic behavior of the stochastic model, also regarding of the value of R0. If R[emailxa0protected]?1, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model, whereas, if R0>1, there is a stationary distribution, which means that the disease will prevail.

The Behavior of an SIR Epidemic Model with Stochastic Perturbation

In this article,we discuss an SIR model with stochastic perturbation. We show that there is a nonnegative solution that belongs to a positively invariant set. Then,by stochastic Lyapunov functional methods,we deduce the globally asymptotical stability and exponential meansquare stability of the disease-free equilibrium under some conditions,which means the disease will die out. Comparing with the deterministic model,there is no endemic equilibrium. To show when the disease will prevail,we investigate the asymptotic behavior of the solution around the endemic equilibrium of the deterministic model. Last,we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments.

Threshold behavior in a stochastic SIQR epidemic model with standard incidence and regime switching

This paper is concerned with the dynamical behavior of a stochastic SIQR epidemic model with standard incidence which is disturbed by both white and telegraph noises. Firstly, we obtain sufficient conditions for persistence in the mean of the disease. Then we establish sufficient conditions for extinction of the disease. In addition, in the case of persistence, we get sufficient conditions for the existence of positive recurrence of the solutions by constructing a suitable stochastic Lyapunov function with regime switching. Meanwhile, the threshold between persistence in the mean and extinction of the stochastic system is also obtained. Finally, some numerical simulations are introduced to demonstrate the analytical results.

The Asymptotic Behavior of a Stochastic Predator-Prey System with Holling II Functional Response

We discuss a stochastic predator-prey system with Holling II functional response. First, we show that this system has a unique positive solution as this is essential in any population dynamics model. Then, we deduce the conditions that there is a stationary distribution of the system, which implies that the system is permanent. At last, we give the conditions for the system that is going to be extinct.

Dynamical behavior of a stochastic HBV infection model with logistic hepatocyte growth

Abstract This paper is concerned with a stochastic HBV infection model with logistic growth. First, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HBV infection model. Then we obtain sufficient conditions for extinction of the disease. The stationary distribution shows that the disease can become persistent in vivo.

The threshold of a stochastic SIS epidemic model with imperfect vaccination

In this paper, we analyze the threshold RvS of a stochastic SIS epidemic model with partially protective vaccination of efficacy e∈[0,1]. Firstly, we show that there exists a unique global positive solution of the stochastic system. Then RvS>1 is verified to be sufficient for persistence in the mean of the system. Furthermore, three conditions for the disease to die out are given, which improve the previously-known results on extinction of the disease. We also obtain that large noise will exponentially suppress the disease from persisting regardless of the value of the basic reproduction number RvS.