A note on advection-diffusion cholera model with bacterial hyperinfectivity

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.