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Stationary distribution of a stochastic cholera model between communities linked by migration

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  • Liu, Qun
  • Jiang, Daqing
  • Hayat, Tasawar
  • Alsaedi, Ahmed
  • Ahmad, Bashir

Abstract

In this paper, we develop and study a stochastic cholera model between communities linked by migration. Firstly, we show that there exists a unique global positive solution of the considered system with any positive initial value. Then by using the stochastic Lyapunov analysis method, we obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Our result shows that the migration and the small white noise are not beneficial for eliminating cholera. Finally, some examples together with numerical simulations are introduced to support the theoretical result.

Suggested Citation

  • Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Stationary distribution of a stochastic cholera model between communities linked by migration," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    • Handle: RePEc:eee:apmaco:v:373:y:2020:i:c:s0096300319310136
    DOI: 10.1016/j.amc.2019.125021
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    References listed on IDEAS

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    8. Sasaki, S. & Suzuki, H. & Fujino, Y. & Kimura, Y. & Cheelo, M., 2009. "Impact of drainage networks on cholera outbreaks in Lusaka, Zambia," American Journal of Public Health, American Public Health Association, vol. 99(11), pages 1982-1987.
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