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

Abstract: This paper presents an SIR epidemic model with two different types of perturbations: white and L\'evy noises. We consecrate to develop a mathematical method to obtain the asymptotic properties of the perturbed model. We use the comparison theorem, mutually exclusive possibilities lemma, and some new techniques of the stochastic differential systems to discuss the following characteristics: persistence in the mean, ergodicity, and extinction of the disease. Finally, numerical simulations about different perturbations are realized to confirm the obtained theoretical results.