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Mathematical Analysis of a Cholera Model with Vaccination

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  • Jing'an Cui
  • Zhanmin Wu
  • Xueyong Zhou

Abstract

We consider a SVR-B cholera model with imperfect vaccination. By analyzing the corresponding characteristic equations, the local stability of a disease-free equilibrium and an endemic equilibrium is established. We calculate the certain threshold known as the control reproduction number . If , we obtain sufficient conditions for the global asymptotic stability of the disease-free equilibrium; the diseases will be eliminated from the community. By comparison of arguments, it is proved that if , the disease persists and the unique endemic equilibrium is globally asymptotically stable, which is obtained by the second compound matrix techniques and autonomous convergence theorems. We perform sensitivity analysis of on the parameters in order to determine their relative importance to disease transmission and show that an imperfect vaccine is always beneficial in reducing disease spread within the community.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnljam:324767
    DOI: 10.1155/2014/324767
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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. Medda, Rakesh & Tiwari, Pankaj Kumar & Pal, Samares, 2024. "Impacts of planktonic components on the dynamics of cholera epidemic: Implications from a mathematical model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 505-526.
    3. 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).

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