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Dynamical behavior and optimal control of a stochastic mathematical model for cholera

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  • Zhou, Xueyong
  • Shi, Xiangyun
  • Wei, Ming

Abstract

A stochastic cholera model with saturation recovery rate is discussed. Firstly, the existence and uniqueness of the global positive solution of the system are proved. Secondly, the asymptotic behavior of the solutions of the stochastic cholera model near the disease-free equilibrium and the corresponding deterministic endemic equilibrium is discussed. Then, the phenomenon that the large noise can cause the extinction of cholera is obtained. Furthermore, on the basis of the stochastic model, the optimal control is added and studied to provide a theoretical basis for the prevention and control of cholera. Finally, the theoretical results are verified by numerical simulations and some suggestions on how to better control the disease are presented.

Suggested Citation

  • Zhou, Xueyong & Shi, Xiangyun & Wei, Ming, 2022. "Dynamical behavior and optimal control of a stochastic mathematical model for cholera," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    • Handle: RePEc:eee:chsofr:v:156:y:2022:i:c:s0960077922000650
    DOI: 10.1016/j.chaos.2022.111854
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    References listed on IDEAS

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    1. Jing'an Cui & Zhanmin Wu & Xueyong Zhou, 2014. "Mathematical Analysis of a Cholera Model with Vaccination," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-16, February.
    2. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Asymptotic behavior of a stochastic delayed SEIR epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 870-882.
    3. O. Chichigina, 2008. "Noise with memory as a model of lemming cycles," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(3), pages 347-352, October.
    4. Ruimin Xu & Rongwei Guo, 2020. "Pontryagin’s Maximum Principle for Optimal Control of Stochastic SEIR Models," Complexity, Hindawi, vol. 2020, pages 1-5, October.
    5. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "The threshold of a stochastic SIS epidemic model with imperfect vaccination," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 78-90.
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    Cited by:

    1. Xueyong Zhou, 2022. "Dynamical Analysis of a Stochastic Cholera Epidemic Model," Mathematics, MDPI, vol. 10(16), pages 1-19, August.
    2. Khatun, Mst Sebi & Mahato, Kiriti Bhusan & Das, Pritha, 2024. "Dynamics of an SuSaV IR epidemic model with stochastic optimal control and awareness programs," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    3. Mandal, Sayan & Samanta, Sudip & Tiwari, Pankaj Kumar & Upadhyay, Ranjit Kumar, 2025. "Bifurcation analysis and exploration of noise-induced transitions of a food chain model with Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 313-338.
    4. Shenxing Li & Wenhe Li, 2024. "Dynamical Behaviors of a Stochastic Susceptible-Infected-Treated-Recovered-Susceptible Cholera Model with Ornstein-Uhlenbeck Process," Mathematics, MDPI, vol. 12(14), pages 1-20, July.
    5. Mukhtar, Roshana & Chang, Chuan-Yu & Raja, Muhammad Asif Zahoor & Chaudhary, Naveed Ishtiaq & Shu, Chi-Min, 2024. "Novel nonlinear fractional order Parkinson's disease model for brain electrical activity rhythms: Intelligent adaptive Bayesian networks," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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