The spreading fronts of an infective environment in a man-environment-man epidemic model
- Authors
- Ahn, Inkyung; Baek, Seunghyeon; Lin, Zhigui
- Issue Date
- 8월-2016
- Publisher
- ELSEVIER SCIENCE INC
- Keywords
- Reaction-diffusion systems; Epidemic model; Free boundary; Spreading and vanishing
- Citation
- APPLIED MATHEMATICAL MODELLING, v.40, no.15-16, pp.7082 - 7101
- Indexed
- SCIE
SCOPUS
- Journal Title
- APPLIED MATHEMATICAL MODELLING
- Volume
- 40
- Number
- 15-16
- Start Page
- 7082
- End Page
- 7101
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/88001
- DOI
- 10.1016/j.apm.2016.02.038
- ISSN
- 0307-904X
- Abstract
- 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 R-0 for the non-spatial epidemic model is defined and the basic reproduction number R-0(F)(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 R-0 <= 1, the bacteria always vanish, and if R-0(F) (t(0)) >= 1 for some t(0) >= 0, the bacteria must spread, while if R-0(F)(0) < 1 < R-0, 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. (C) 2016 Elsevier Inc. All rights reserved.
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Collections - College of Science and Technology > Data Computational Sciences in Division of Applied Mathematical Sciences > 1. Journal Articles
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