### Mathematical Biosciences and Engineering

2020, Issue 6: 7398-7410. doi: 10.3934/mbe.2020378
Research article

# A note on advection-diffusion cholera model with bacterial hyperinfectivity

• 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.

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

### Related Papers:

• 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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