Abstract
In this paper, we consider an impulsive SIR model with incidence rate stochastically perturbed. First, we prove the existence and uniqueness of the global positive solution by constructing the equivalent system without impulse. Second, we obtain a sufficient condition which determines epidemic to extinct. Then we demonstrate the existence and global attraction of the boundary periodic solution under the certain condition. Finally, we present a sufficient condition which allows the existence of a positive periodic solution. (C) 2018 Elsevier B.V. All rights reserved.