Transmission dynamics of cholera with hyperinfectious and hypoinfectious vibrios: mathematical modelling and control strategies

Jiazhe Lin; Rui Xu; Xiaohong Tian; Jiazhe Lin; Rui Xu; Xiaohong Tian

doi:10.3934/mbe.2019216

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 4339-4358. doi: 10.3934/mbe.2019216

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Transmission dynamics of cholera with hyperinfectious and hypoinfectious vibrios: mathematical modelling and control strategies

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

Received: 02 February 2019 Accepted: 25 April 2019 Published: 16 May 2019

Cholera is a common infectious disease caused by Vibrio cholerae, which has different infectivity. In this paper, we propose a cholera model with hyperinfectious and hypoinfectious vibrios, in which both human-to-human and environment-to-human transmissions are considered. By analyzing the characteristic equations, the local stability of disease-free and endemic equilibria is established. By using Lyapunov functionals and LaSalleos invariance principle, it is verified that the global threshold dynamics of the model can be completely determined by the basic reproduction number. Numerical simulations are carried out to illustrate the corresponding theoretical results and describe the cholera outbreak in Haiti. The study of optimal control helps us seek cost-effective solutions of time-dependent control strategies against cholera outbreaks, which shows that control strategies, such as vaccination and sanitation, should be taken at the very beginning of the outbreak and become less necessary after a certain period.
- Cholera model,
- hyperinfectious vibrios,
- human-to-human transmission,
- environment-to-human transmission,
- global dynamics,
- optimal control
Citation: Jiazhe Lin, Rui Xu, Xiaohong Tian. Transmission dynamics of cholera with hyperinfectious and hypoinfectious vibrios: mathematical modelling and control strategies[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 4339-4358. doi: 10.3934/mbe.2019216

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Abstract

Cholera is a common infectious disease caused by Vibrio cholerae, which has different infectivity. In this paper, we propose a cholera model with hyperinfectious and hypoinfectious vibrios, in which both human-to-human and environment-to-human transmissions are considered. By analyzing the characteristic equations, the local stability of disease-free and endemic equilibria is established. By using Lyapunov functionals and LaSalleos invariance principle, it is verified that the global threshold dynamics of the model can be completely determined by the basic reproduction number. Numerical simulations are carried out to illustrate the corresponding theoretical results and describe the cholera outbreak in Haiti. The study of optimal control helps us seek cost-effective solutions of time-dependent control strategies against cholera outbreaks, which shows that control strategies, such as vaccination and sanitation, should be taken at the very beginning of the outbreak and become less necessary after a certain period.

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