Stability analysis and asymptotic behavior of a stochastic delayed SIRS epidemic model with a class of nonlinear incidence rates
Abstract
This paper deals with a stochastic version of a deterministic delayed SIRS (Susceptible-InfectiveRemoved-Suceptible) epidemic model with nonlinear incidence rate. The stochastic model is obtained by taking into account random perturbations in the contact rate β due to environmental variations. We assume that the stochastic perturbation intensity is proportional to the number of infectious. Firstly, the existence of a unique global positive solution of the stochastic differential equations with delay describing the model is proved. Then, the stability of the disease-free equilibrium point is established under suitable conditions on the parameters of the model. We also study the asymptotic behaviour of the solution when the disease-free equilibrium (DFE) is unstable. Finally, numerical simulations are introduced to support our results.
- Published
- 11 August 2025
- Volume
- 2025 (2025)
- License
- CC BY 3.0
Copyright © 2025 Boubacar Sidiki Kouyaté, Modeste N'Zi. 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
B. S. Kouyaté, M. N'Zi, Stability analysis and asymptotic behavior of a stochastic delayed SIRS epidemic model with a class of nonlinear incidence rates, Commun. Math. Biol. Neurosci. 2025 (2025), 100. https://doi.org/10.28919/cmbn/9373
BibTeX
@article{Kouyaté2025,
author = {Kouyaté, Boubacar Sidiki and N'Zi, Modeste},
title = {Stability analysis and asymptotic behavior of a stochastic delayed SIRS epidemic model with a class of nonlinear incidence rates},
journal = {Commun. Math. Biol. Neurosci.},
volume = {2025},
year = {2025},
pages = {100},
doi = {10.28919/cmbn/9373}
}