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A control treatment for a stochastic epidemic model with relapse and Crowly–Martin incidence

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Abstract

In this paper, we study a stochastic epidemic model with relapse, non linear incidence and a random transmission rate. The existence, uniqueness and boundedness of a positive solution are proved for any positive initial value. Using the Lyapunov analysis, we investigate the asymptotic behaviour of the solution. Mainly, we give sufficient conditions for extinction and persistence of the disease. Then, we propose an optimal control for both deterministic and stochastic models. Finally, we give some numerical illustrations to demonstrate 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 laboratory MAD (Management de l’agriculture Durable) of EST Sidi Bannour and the Faculty of sciences, Ibn Tofail University, Kenitra for their help and support.

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The authors received no specific funding for this work.

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Authors and Affiliations

  1. Laboratory of PDE’s, Algebra and Spectral Geometry, Faculty of Sciences, Ibn Tofail University, BP 133, Kenitra, Morocco

    M. El Fatini, I. Sekkak & T. El Guendouz

  2. Chouaib Doukkali University, EST-Sidi Bennour, El Jadida, Morocco

    R. Taki

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  1. M. El Fatini
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  2. I. Sekkak
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  3. R. Taki
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  4. T. El Guendouz
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Correspondence to M. El Fatini.

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El Fatini, M., Sekkak, I., Taki, R. et al. A control treatment for a stochastic epidemic model with relapse and Crowly–Martin incidence. J Anal 29, 713–729 (2021). https://doi.org/10.1007/s41478-020-00276-4

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  • DOI: https://doi.org/10.1007/s41478-020-00276-4

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