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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 5620301, 9 pages
https://doi.org/10.1155/2017/5620301
Research Article

The Threshold of a Stochastic SIRS Model with Vertical Transmission and Saturated Incidence

School of Mathematics and Statistics, Shaoguan University, Shaoguan 512005, China

Correspondence should be addressed to Yufeng Sun; moc.anis@1002ynus

Received 27 January 2016; Accepted 15 November 2016; Published 28 February 2017

Academic Editor: Manuel De la Sen

Copyright © 2017 Chunjuan Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The threshold of a stochastic SIRS model with vertical transmission and saturated incidence is investigated. If the noise is small, it is shown that the threshold of the stochastic system determines the extinction and persistence of the epidemic. In addition, we find that if the noise is large, the epidemic still prevails. Finally, numerical simulations are given to illustrate the results.