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Mathematical analysis of a cholera infection model with vaccination strategy

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  • Tian, Xiaohong
  • Xu, Rui
  • Lin, Jiazhe

Abstract

In this paper, a cholera infection model with vaccination strategy is investigated. By analyzing corresponding characteristic equations, the local stability of each of feasible equilibria is established. By means of Lyapunov functions and LaSalle’s invariance principle, it is proved that if the basic reproduction number is less than unity, the disease-free equilibrium is globally asymptotically stable. If the basic reproduction number is greater than unity, the endemic equilibrium is globally asymptotically stable. In addition, by using Pontryagin’s maximum principle, several reasonable optimal control strategies are suggested to the prevention and control of the cholera infection. Numerical simulations are carried out to illustrate the theoretical results.

Suggested Citation

  • Tian, Xiaohong & Xu, Rui & Lin, Jiazhe, 2019. "Mathematical analysis of a cholera infection model with vaccination strategy," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 517-535.
    • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:517-535
    DOI: 10.1016/j.amc.2019.05.055
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    1. Michael McAsey & Libin Mou & Weimin Han, 2012. "Convergence of the forward-backward sweep method in optimal control," Computational Optimization and Applications, Springer, vol. 53(1), pages 207-226, September.
    2. Joshua Kiddy K. Asamoah & Francis T. Oduro & Ebenezer Bonyah & Baba Seidu, 2017. "Modelling of Rabies Transmission Dynamics Using Optimal Control Analysis," Journal of Applied Mathematics, Hindawi, vol. 2017, pages 1-23, July.
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    Cited by:

    1. Sharma, Sandeep & Singh, Fateh, 2021. "Bifurcation and stability analysis of a cholera model with vaccination and saturated treatment," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Zhou, Baoquan & Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Ergodic stationary distribution and extinction of a hybrid stochastic SEQIHR epidemic model with media coverage, quarantine strategies and pre-existing immunity under discrete Markov switching," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    3. Juan Shen & Xiao Tu & Yuanyuan Li, 2023. "Mathematical Modeling Reveals Mechanisms of Cancer-Immune Interactions Underlying Hepatocellular Carcinoma Development," Mathematics, MDPI, vol. 11(20), pages 1-30, October.

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