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The Threshold of a Stochastic SIRS Epidemic Model with a General Incidence

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Abstract

In this article, a SIRS epidemic model with a general incidence rate is proposed and investigated. We briefly verify the global existence of a unique positive solution for the proposed system. Moreover, and unlike other works, we were able to find the stochastic threshold \(\mathcal {R}_s\) of the proposed model which was used for the discussion of the persistence in mean and extinction of the disease. Moreover, we utilize stochastic Lyapunov functions to show under sufficient conditions the existence and uniqueness of stationary distributions of the solution. Lastly, numerical simulation is executed to conform our analytical results.

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Acknowledgements

The authors are very grateful to the Editor and the Reviewers for their helpful and constructive comments and suggestions. The authors are also thankful to the the Faculty of sciences, Ibn Tofail University, Kenitra and the laboratory MFA (Mathématiques Fondamentales et Applications) Faculty of sciences, Chouaib Doukkali University, El Jadida for their help and support.

Funding

This work is Funded by Ministerio de Ciencia e Innovación (Spain) and FEDER (European Community) under grant PID2021-122991NB-C21.

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Authors and Affiliations

  1. Department of Computer & Mathematics, Chouaib Doukkali University, EST- Sidi Bennour, El jadida, Morocco

    Regragui Taki

  2. Department of Mathematics, Ibn Tofail University, FS, Kénitra, BP, 133, Morocco

    Mohammed Lakhal, Tarik El Guendouz & Mohamed El Fatini

Authors
  1. Mohammed Lakhal
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  2. Tarik El Guendouz
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  3. Regragui Taki
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  4. Mohamed El Fatini
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Correspondence to Regragui Taki.

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Communicated by Rosihan M. Ali.

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Lakhal, M., Guendouz, T.E., Taki, R. et al. The Threshold of a Stochastic SIRS Epidemic Model with a General Incidence. Bull. Malays. Math. Sci. Soc. 47, 100 (2024). https://doi.org/10.1007/s40840-024-01696-2

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  • DOI: https://doi.org/10.1007/s40840-024-01696-2

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