### Mathematical Biosciences and Engineering

2020, Issue 4: 4210-4224. doi: 10.3934/mbe.2020233
Research article

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

• 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.

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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• 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.

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• © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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