A note on advection-diffusion cholera model with bacterial hyperinfectivity

Xiaoqing Wu; Yinghui Shan; Jianguo Gao; Xiaoqing Wu; Yinghui Shan; Jianguo Gao

doi:10.3934/mbe.2020378

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 7398-7410. doi: 10.3934/mbe.2020378

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Research article

A note on advection-diffusion cholera model with bacterial hyperinfectivity

Department of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China

Received: 15 August 2020 Accepted: 18 October 2020 Published: 28 October 2020

This note gives a supplement to the recent work of Wang and Wang (2019) in the sense that: (ⅰ) for the critical case where $\Re_{0} = 1$, cholera-free steady state is globally asymptotically stable; (ⅱ) in a homogeneous case, the positive constant steady-state is globally asymptotically stable with additional condition when $\Re_{0}>1$. Our first result is achieved by proving the local asymptotic stability and global attractivity. Our second result is obtained by Lyapunov function.
- advection-diffusion cholera model,
- hyperinfectivity,
- spatial heterogeneity,
- basic reproduction number,
- global stability
Citation: Xiaoqing Wu, Yinghui Shan, Jianguo Gao. A note on advection-diffusion cholera model with bacterial hyperinfectivity[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 7398-7410. doi: 10.3934/mbe.2020378

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Abstract

This note gives a supplement to the recent work of Wang and Wang (2019) in the sense that: (ⅰ) for the critical case where $\Re_{0} = 1$, cholera-free steady state is globally asymptotically stable; (ⅱ) in a homogeneous case, the positive constant steady-state is globally asymptotically stable with additional condition when $\Re_{0}>1$. Our first result is achieved by proving the local asymptotic stability and global attractivity. Our second result is obtained by Lyapunov function.

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