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Bifurcation and stability analysis of a cholera model with vaccination and saturated treatment

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  • Sharma, Sandeep
  • Singh, Fateh

Abstract

In this paper, we proposed a new deterministic cholera model with two control measures namely; vaccination and treatment. It is assumed that vaccination is perfect and hence vaccinated individuals do not contribute to the infected population. The model considers a saturated treatment function. This is realistic as cholera mostly affects the developing and underdeveloped countries which have limited treatment facilities. The control reproduction number (Rc) for the proposed model has been obtained using the next generation matrix method. There exist multiple equilibrium points as the proposed model undergoes backward bifurcation when Rc<1. The result for the global stability of the endemic equilibrium point is obtained using the compound matrix technique. Extensive numerical simulation is performed to illustrate theoretical results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002666
    DOI: 10.1016/j.chaos.2021.110912
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    References listed on IDEAS

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    1. Liu, Junli & Zhang, Tailei, 2009. "Bifurcation analysis of an SIS epidemic model with nonlinear birth rate," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1091-1099.
    2. 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.
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