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.