Developing New Techniques for Obtaining the Threshold of a Stochastic SIR Epidemic Model with 3-Dimensional Levy Process

This paper considers the classical SIR epidemic model driven by a multidimensional Levy jump process. We consecrate to develop mathematical method obtain asymptotic properties of perturbed model. Our differs from previous approaches use comparison theorem, mutually exclusive possibilities lemma, and some new techniques stochastic differential systems. In this framework, we derive threshold which can determine existence unique ergodic stationary distribution or extinction epidemic. Numerical simulations about different perturbations are realized confirm obtained theoretical results.