Open AccessA spatial SIS model in heterogeneous environments with vary advective rate
Author(s) -
An Xu,
Xianfa Song
Publication year - 2021
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.2021276
Subject(s) - advection , stability (learning theory) , basic reproduction number , diffusion , spatial heterogeneity , mathematics , statistical physics , exponential stability , physics , computer science , ecology , biology , thermodynamics , demography , quantum mechanics , machine learning , sociology , population , nonlinear system
We study a spatial susceptible-infected-susceptible(SIS) model in heterogeneous environments with vary advective rate. We establish the asymptotic stability of the unique disease-free equilibrium(DFE) when $ \mathcal{R}_0 < 1 $ and the existence of the endemic equilibrium when $ \mathcal{R}_0 > 1 $. Here $ \mathcal{R}_0 $ is the basic reproduction number. We also discuss the effect of diffusion on the stability of the DFE.