Asymptotic Behavior of a Stochastic SIRS Model with Non-linear Incidence and Levy Jumps

A stochastic susceptible-infective-recovered-susceptible( SIRS) model with non-linear incidence and Levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ultimate boundedness of the solution of the model was obtained by using the method of Lyapunov function and the generalized Ito's formula. At last,asymptotic behaviors of the solution were discussed according to the value of R0. If R0< 1,the solution of the model oscillates around a steady state, which is the diseases free equilibrium of the corresponding deterministic model,and if R0> 1,it fluctuates around the endemic equilibrium of the deterministic model.

AN AVERAGING PRINCIPLE FOR STOCHASTIC DIFFERENTIAL DELAY EQUATIONS DRIVEN BY TIME-CHANGED LéVY NOISE

In this paper,we aim to derive an averaging principle for stochastic differential equations driven by time-changed Lévy noise with variable delays.Under certain assumptions,we show that the solutions of stochastic differential equations with time-changed Lévy noise can be approximated by solutions of the associated averaged stochastic differential equations in mean square convergence and in convergence in probability,respectively.The convergence order is also estimated in terms of noise intensity.Finally,an example with numerical simulation is given to illustrate the theoretical result.

Dynamic characterization of a stochastic SIR infectious disease model with dual perturbation

Environmental perturbations are unavoidable in the propagation of infectious diseases.In this paper,we introduce the stochasticity into the susceptible-infected recovered(SIR)model via thc^parameter perturbation method.The stochastic disturbances associated with the disease transmission coefficient and the mortality rate are presented with two perturbations:Gaussian white noise and Levy jumps,respectively.This idea provides an overview of disease dynamics under different random perturbation scenarios.By using new techniques and methods,we study certain interesting asymptotic properties of our perturbed model,namely:persistence in the mean,ergodicity and extinction of the disease.For illustrative purposes,numerical examples are presented for checking the theoretical study.

Dynamic of a stochastic delayed one-predator two-prey model with Lévy jumps in polluted environments

This paper is concerned with a stochastic delayed one-predator two-prey model with Lévy jumps in polluted environments.First,under some simple assumptions,we prove that there exists a unique global nonnegative solution which is permanent in time average.Moreover,sufficient criteria for the extinction of each species are obtained.Finally,we carry out some numerical simulations to verify the theoretical results.

Analysis on stochastic dynamics of two-consumers-one-resource competing systems with Beddington-DeAngelis functional response

In this paper,stochastic dynamics with Lévy noise of two-consumers-one-resource competing systems with Beddington–DeAngelis functional response are considered.We first show the existence of the global positive solution,then discuss the effects of noises on the extinction of the species and the stochastic persistence of the species.In the meanwhile,numerical simulations are carried to support results.Finally,we show the existence of the stationary distribution for a special case.