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

In this paper, Brownian motion and L e ́ vy 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 , R ̄ 0 are showed. We find that if R ˜ 0 < 1 , the disease may die out, and when R ̄ 0 > 1 , the disease may be persistent. Finally, the numerical simulations are presented to illustrate our mathematical results. [ABSTRACT FROM AUTHOR]