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Rapid Diagnosis of Avian Influenza Virus in Wild Birds: Use of a Portable rRT-PCR and Freeze-dried Reagents in the Field
Published on: August 2, 2011
The spreading frontiers of avian-human influenza described by the free boundary
ChengXia Lei1, KwangIk Kim2, ZhiGui Lin1
11School of Mathematical Science, Yangzhou University, Yangzhou, 225002 China.
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 (t) and R 0 (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 (0) < 1 and the initial number of the infected birds is small, the avian influenza vanishes in the bird world. Furthermore, if r 0 (0) < 1 and R 0 (0) < 1, the avian influenza vanishes in the bird and human worlds. In the case that r 0 (0) < 1 and R 0 (0) > 1, spreading of the mutant avian influenza in the human world is possible. It is also shown that if r 0 (t 0) ⩾ 1 for any t 0 ⩾ 0, the avian influenza spreads in the bird world.
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