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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 517439, 12 pages
http://dx.doi.org/10.1155/2013/517439
Research Article

Dynamics of Stochastically Perturbed SIS Epidemic Model with Vaccination

1School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, China
2School of Science, Changchun University, Changchun, Jilin 130022, China

Received 2 February 2013; Revised 12 July 2013; Accepted 12 July 2013

Academic Editor: Julio Rossi

Copyright © 2013 Yanan Zhao and Daqing Jiang. 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

We introduce stochasticity into an SIS epidemic model with vaccination. The stochasticity in the model is a standard technique in stochastic population modeling. In the deterministic models, the basic reproduction number is a threshold which determines the persistence or extinction of the disease. When the perturbation and the disease-related death rate are small, we carry out a detailed analysis on the dynamical behavior of the stochastic model, also regarding of the value of . If , the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model, whereas, if , there is a stationary distribution, which means that the disease will prevail. The results are illustrated by computer simulations.