Global dynamics and optimal control of a cholera transmission model with vaccination strategy and multiple pathways

Chenwei Song; Rui Xu; Ning Bai; Xiaohong Tian; Jiazhe Lin; Chenwei Song; Rui Xu; Ning Bai; Xiaohong Tian; Jiazhe Lin

doi:10.3934/mbe.2020233

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 4: 4210-4224. doi: 10.3934/mbe.2020233

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Research article

Global dynamics and optimal control of a cholera transmission model with vaccination strategy and multiple pathways

1.
Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, P. R. China
2.
Institute of Applied Mathematics, Army Engineering University, Shijiazhuang 050003, Hebei, P. R. China

Received: 01 May 2020 Accepted: 09 June 2020 Published: 15 June 2020

In this paper, we consider a cholera infection model with vaccination and multiple transmission pathways. Dynamical properties of the model are analyzed in detail. It is shown that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity; the endemic equilibrium exists and is globally asymptotically stable if the basic reproduction number is greater than unity. In addition, the model is successfully used to fit the real disease situation of cholera outbreak in Somalia. We consider an optimal control problem of cholera transmission with vaccination, quarantine, treatment and sanitation control strategies, and use Pontryagin's minimum principle to determine the optimal control level. The optimal control problem is solved numerically.
- cholera infection,
- vaccination,
- multiple pathways,
- stability,
- optimal control
Citation: Chenwei Song, Rui Xu, Ning Bai, Xiaohong Tian, Jiazhe Lin. Global dynamics and optimal control of a cholera transmission model with vaccination strategy and multiple pathways[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 4210-4224. doi: 10.3934/mbe.2020233

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Abstract

In this paper, we consider a cholera infection model with vaccination and multiple transmission pathways. Dynamical properties of the model are analyzed in detail. It is shown that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity; the endemic equilibrium exists and is globally asymptotically stable if the basic reproduction number is greater than unity. In addition, the model is successfully used to fit the real disease situation of cholera outbreak in Somalia. We consider an optimal control problem of cholera transmission with vaccination, quarantine, treatment and sanitation control strategies, and use Pontryagin's minimum principle to determine the optimal control level. The optimal control problem is solved numerically.

References

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