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Conditions for Permanence and Ergodicity of Certain SIR Epidemic Models

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Abstract

In this paper, we study sufficient conditions for the permanence and ergodicity of a stochastic susceptible-infected-recovered (SIR) epidemic model with Beddington-DeAngelis incidence rate in both of non-degenerate and degenerate cases. The conditions obtained in fact are close to the necessary one. We also characterize the support of the invariant probability measure and prove the convergence in total variation norm of the transition probability to the invariant measure. Some of numerical examples are given to illustrate our results.

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Acknowledgements

We gratefully thank the reviewers and the editor for their positive and helpful suggestions, which help to improve the presentation of the paper. Authors would like to express our gratitude to Nguyen Hai Dang for his valuable comments which helped to improve the paper. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.03-2017.23.

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Authors and Affiliations

  1. Department of Mathematics, Mechanics and Informatics, Hanoi National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

    Nguyen Huu Du & Nguyen Ngoc Nhu

  2. Department of Mathematics, Vinh University, 182 Le Duan, Vinh, Nghe An, Vietnam

    Nguyen Thanh Dieu

Authors
  1. Nguyen Huu Du
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  2. Nguyen Thanh Dieu
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  3. Nguyen Ngoc Nhu
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Correspondence to Nguyen Thanh Dieu.

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Authors would like to thank Vietnam Institute for Advance Study in Mathematics (VIASM) for supporting and providing a fruitful research environment and hospitality.

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Du, N.H., Dieu, N.T. & Nhu, N.N. Conditions for Permanence and Ergodicity of Certain SIR Epidemic Models. Acta Appl Math 160, 81–99 (2019). https://doi.org/10.1007/s10440-018-0196-8

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  • DOI: https://doi.org/10.1007/s10440-018-0196-8

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