The spreading frontiers of avian-human influenza described by the free boundary
SCIE
SCOPUS
- Title
- The spreading frontiers of avian-human influenza described by the free boundary
- Authors
- Lei, CX; Kim, K; Lin, ZG
- Date Issued
- 2014-05
- Publisher
- SCIENCE PRESS
- Abstract
- In this paper, a reaction-diffusion system is proposed to investigate avian-human influenza. Two free boundaries are introduced to describe the spreading frontiers of the avian influenza. The basic reproduction numbers r (0) (F) (t) and R (0) (F) (t) are defined for the bird with the avian influenza and for the human with the mutant avian influenza of the free boundary problem, respectively. Properties of these two time-dependent basic reproduction numbers are obtained. Sufficient conditions both for spreading and for vanishing of the avian influenza are given. It is shown that if r (0) (F) (0) < 1 and the initial number of the infected birds is small, the avian influenza vanishes in the bird world. Furthermore, if r (0) (F) (0) < 1 and R (0) (F) (0) < 1, the avian influenza vanishes in the bird and human worlds. In the case that r (0) (F) (0) < 1 and R (0) (F) (0) > 1, spreading of the mutant avian influenza in the human world is possible. It is also shown that if r (0) (F) (t (0)) a (c) 3/4 1 for any t (0) a (c) 3/4 0, the avian influenza spreads in the bird world.
- Keywords
- reaction-diffusion system; avian-human influenza; free boundary; spreading frontiers; EPIDEMIC MODEL; INFECTIOUS-DISEASES; MATHEMATICAL-THEORY; SARS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/14117
- DOI
- 10.1007/S11425-013-4652-7
- ISSN
- 1674-7283
- Article Type
- Article
- Citation
- SCIENCE CHINA-MATHEMATICS, vol. 57, no. 5, page. 971 - 990, 2014-05
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