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. 2013 May 29;57(5):971–990. doi: 10.1007/s11425-013-4652-7

The spreading frontiers of avian-human influenza described by the free boundary

ChengXia Lei 1, KwangIk Kim 2, ZhiGui Lin 1,✉
PMCID: PMC7089280  PMID: 32214993

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 F0 (t) and R F0(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 F0 (0) < 1 and the initial number of the infected birds is small, the avian influenza vanishes in the bird world. Furthermore, if r F0 (0) < 1 and R F0(0) < 1, the avian influenza vanishes in the bird and human worlds. In the case that r F0 (0) < 1 and R F0(0) > 1, spreading of the mutant avian influenza in the human world is possible. It is also shown that if r F0 (t 0) ⩾ 1 for any t 0 ⩾ 0, the avian influenza spreads in the bird world.

Keywords: reaction-diffusion system, avian-human influenza, free boundary, spreading frontiers

Contributor Information

ChengXia Lei, Email: leichengxia001@163.com.

KwangIk Kim, Email: kimki@postech.ac.kr.

ZhiGui Lin, Email: zglin68@hotmail.com.

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