Dynamical behaviors of a stochastic SIRS epidemic model

Amine EL Koufi, Jihad Adnani, Abdelkrim Bennar, Noura Yousfi

Abstract


In this paper, we study the dynamical behavior of a stochastic SIRS epidemic model with specific nonlinear incidence rate and vaccination. We show the existence and positivity of the solution of the SIRS stochastic differential equation. We defined a number $\mathcal{R}$ and we prove the disease free equilibrium is almost sure exponentially stable if $\mathcal{R}<1$. We studying the behavior around the endemic equilibrium E*. Numerical simulations presented our theoretical results.

Full Text: PDF

How to Cite this Article:

Amine EL Koufi, Jihad Adnani, Abdelkrim Bennar, Noura Yousfi, Dynamical behaviors of a stochastic SIRS epidemic model, Journal of Mathematical and Computational Science, Vol 8, No 3 (2018), 421-436

Copyright © 2018 Amine EL Koufi, Jihad Adnani, Abdelkrim Bennar, Noura Yousfi. 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.

J. Math. Comput. Sci.

ISSN: 1927-5307

Editorial Office: jmcs@scik.org

 

Copyright ©2018 JMCS