Dynamical behaviors of a stochastic SIRS epidemic model
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.
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.
Cite this article
A. EL Koufi, J. Adnani, A. Bennar, N. Yousfi, Dynamical behaviors of a stochastic SIRS epidemic model, J. Math. Comput. Sci. 8 (2018), 421–436. https://doi.org/10.28919/jmcs/3658
BibTeX
@article{Koufi2018,
author = {EL Koufi, Amine and Adnani, Jihad and Bennar, Abdelkrim and Yousfi, Noura},
title = {Dynamical behaviors of a stochastic SIRS epidemic model},
journal = {J. Math. Comput. Sci.},
volume = {8},
year = {2018},
pages = {421--436},
doi = {10.28919/jmcs/3658}
}