Global stability and positive recurrence of a stochastic SIS model with Lévy noise perturbation

Abstract

Focusing on epidemic model in random environments, this paper uses white noise and Lévy noise to model the dynamics of the SIS epidemic model subject to the random changes of the external environment. We show that the jump encourages the extinction of the disease in the population. We first, give a rigorous proof of the global stability of the disease-free equilibrium state. We also establish sufficient conditions for the persistence of the disease. The presented results are demonstrated by numerical simulations.