The threshold of a stochastic SIVS epidemic model with nonlinear saturated incidence

A stochastic version of the SIS epidemic model with vaccination (SIVS) is studied. When the noise is small, the threshold parameter is identified, which determines the extinction and persistence of the epidemic. Besides, the results show that large noise will suppress the epidemic from prevailing regardless of the saturated incidence. The results are illustrated by computer simulations. (C) 2015 Elsevier B.V. All rights reserved.