A stochastic SIS epidemic infectious diseases model with double stochastic perturbations

Abstract

In this paper, a stochastic SIS epidemic infectious diseases model with double stochastic perturbations is proposed. First, the existence and uniqueness of the positive global solution of the model are proved. Second, the controlling conditions for the extinction and persistence of the disease are obtained. Besides, the effects of the intensity of volatility [Formula: see text] and the speed of reversion [Formula: see text] on the dynamical behaviors of the model are discussed. Finally, some numerical examples are given to support the theoretical results. The results show that if the basic reproduction number [Formula: see text], the disease will be extinct, that is to say that we can control the threshold [Formula: see text] to suppress the disease outbreak.