Open AccessA note on advection-diffusion cholera model with bacterial hyperinfectivity
Author(s) -
Xulong Wu,
Yinghui Shan,
Jianguo Gao
Publication year - 2020
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2020378
Subject(s) - lyapunov function , mathematics , exponential stability , advection , constant (computer programming) , stability theory , steady state (chemistry) , stability (learning theory) , homogeneous , diffusion , state (computer science) , work (physics) , mathematical analysis , physics , computer science , nonlinear system , combinatorics , chemistry , quantum mechanics , machine learning , thermodynamics , programming language , algorithm
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.