2014/08/27 by Inkyung Ahn, Ahn, Inkyung, Zhigui Lin +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Analysis of PDEs (math.AP) #COVID-19 epidemiological studies #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #math.AP
paper · pdf · doi:10.48550/arxiv.1408.6326
23 pages
arxiv created 2014/08/27 · openalex publication_date 2014/08/27 · arxiv updated 2014/08/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A reaction-diffusion model is investigated to understand infective environments in a man-environment-man epidemic model. The free boundary is introduced to describe the expanding front of an infective environment induced by fecally-orally transmitted disease. The basic reproduction number RF0(t) for the free boundary problem is introduced, and the behavior of positive solutions to the reaction-diffusion system is discussed. Sufficient conditions for the bacteria to vanish or spread are given. We show that, if R0≤ 1, the bacteria always vanish, and if RF0(t0)≥ 1 for some t0≥ 0, the bacteria must spread, while if RF0(0)<1<R0, the spreading or vanishing of the bacteria depends on the initial number of bacteria, the length of the initial habitat, the diffusion rate, and other factors. Moreover, some sharp criteria are given.