Extinction and persistence of a stochastic nonlinear SIS epidemic model with jumps

In this paper, Brownian motion and Lévy jumps are introduced to a SIS type epidemic model with nonlinear incidence rate. The dynamical behavior of the considered model is investigated. In order to reveal the extinction and permanence of the disease, two threshold values R˜0,R̄0 are showed. We find that if R˜0<1, the disease may die out, and when R̄0>1, the disease may be persistent. Finally, the numerical simulations are presented to illustrate our mathematical results.