Open AccessAnalysis of a diffusive cholera model incorporating latency and bacterial hyperinfectivity
Author(s) -
Wei Yang,
Jinliang Wang
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021138
Subject(s) - eigenvalues and eigenvectors , constant (computer programming) , dynamics (music) , cholera , mathematics , latency (audio) , basic reproduction number , lyapunov function , statistical physics , computer science , physics , quantum mechanics , telecommunications , nonlinear system , population , demography , sociology , acoustics , microbiology and biotechnology , biology , programming language
In this paper, we are concerned with the threshold dynamics of a diffusive cholera model incorporating latency and bacterial hyperinfectivity. Our model takes the form of spatially nonlocal reaction-diffusion system associated with zero-flux boundary condition and time delay. By studying the associated eigenvalue problem, we establish the threshold dynamics that determines whether or not cholera will spread. We also confirm that the threshold dynamics can be determined by the basic reproduction number. By constructing Lyapunov functional, we address the global attractivity of the unique positive equilibrium whenever it exists. The theoretical results are still hold for the case when the constant parameters are replaced by strictly positive and spatial dependent functions.