Threshold dynamics of a stochastic SIS epidemic model with nonlinear incidence rate

In this paper, we study a stochastic SIS epidemic model with nonlinear incidence rate. By employing the Markov semigroups theory, we verify that the reproduction number R-0 - sigma(2)Lambda(2)f(2)(Lambda/mu, 0)/2 mu(2)(mu+gamma+alpha) can be used to govern the threshold dynamics of the studied system. If R-0 - sigma(2)Lambda(2)f(2)(Lambda/mu 0)/2 mu(2)(mu+gamma+alpha) > 1, we show that there is a unique stable stationary distribution and the densities of the distributions of the solutions can converge in L-1 to an invariant density. R-0 - sigma(2)Lambda(2)f(2)(Lambda/mu 0)/2 mu(2)(mu+gamma+alpha) < 1, under mild extra conditions, we establish sufficient conditions for extinction of the epidemic. Our results show that larger white noise can lead to the extinction of the epidemic while smaller white noise can ensure the existence of a stable stationary distribution which leads to the stochastic persistence of the epidemic. (C) 2019 Elsevier B.V. All rights reserved.