Abstract
In this paper, we include stochastic perturbations into SIR and SEIR epidemic models with saturated incidence and investigate their dynamics according to the basic reproduction number R-0. The long time behavior of the two stochastic systems is studied. Mainly, we utilize stochastic Lyapunov functions to show under some conditions, the solution has the ergodic property as R-0 > 1, while exponential stability as R-0 <= 1. At last, we make simulations to conform our analytical results. (C) 2011 Elsevier Inc. All rights reserved.