International Journal of Stochastic Analysis
Volume 2013 (2013), Article ID 431257, 4 pages
http://dx.doi.org/10.1155/2013/431257
Research Article

Stability Analysis of a Stochastic SIR Epidemic Model with Specific Nonlinear Incidence Rate

Jihad Adnani,1 Khalid Hattaf,1,2 and Noura Yousfi1

1Department of Mathematics and Computer Science, Faculty of Sciences Ben M'sik, Hassan II University, P.O. Box 7955, Sidi Othman, Casablanca, Morocco
2Centre Régional des Métiers de l'Education et de la Formation (CRMEF), Derb Ghalef, Casablanca, Morocco

Received 30 May 2013; Accepted 21 August 2013

Academic Editor: Josefa Linares-Pérez

Copyright © 2013 Jihad Adnani 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

We investigate a stochastic SIR epidemic model with specific nonlinear incidence rate. The stochastic model is derived from the deterministic epidemic model by introducing random perturbations around the endemic equilibrium state. The effect of random perturbations on the stability behavior of endemic equilibrium is discussed. Finally, numerical simulations are presented to illustrate our theoretical results.