Open AccessThe SIS model with diffusion of virus in the environment
Author(s) -
Dan Feng Pang,
Yan Xiao
Publication year - 2019
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.2019141
Subject(s) - traveling wave , diffusion , transmission (telecommunications) , perturbation (astronomy) , homogeneous , basic reproduction number , reaction–diffusion system , wave speed , disease transmission , mathematics , mathematical analysis , statistical physics , physics , biological system , computer science , biology , virology , demography , telecommunications , quantum mechanics , population , sociology
In this paper, we propose an SIS-type reaction-diffusion equations, which contains both direct transmission and indirect transmission via free-living and spatially diffusive bacteria/virus in the contaminated environment, motivated by the dynamics of hospital infections. We establish the basic reproduction number R ₀ which can act as threshold level to determine whether the disease persists or not. In particular, if R ₀<1 then ="" the ="" disease-free ="" equilibrium ="" is ="" globally ="" asymptotically ="" stable ="" whereas ="". For the spatially homogeneous system, we investigate the traveling wave solutions and obtain that there exists a critical wave speed, below which there has no traveling waves, above which the traveling wave solutions may exist for small diffusion coefficient by the geometric singular perturbation method. The finding implies that great spatial transmission leads to an increase in new infection, while large diffusion of bacteria/virus results in the new infection decline for spatially heterogeneous environment.