Lei ChengXia, Kim KwangIk, Lin ZhiGui
1School of Mathematical Science, Yangzhou University, Yangzhou, 225002 China.
2Department of Mathematics, Pohang University of Science and Technology, Pohang, 790-784 Republic of Korea.
Sci China Math. 2014;57(5):971-990. doi: 10.1007/s11425-013-4652-7. Epub 2013 May 29.
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 () and () 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 (0) < 1 and the initial number of the infected birds is small, the avian influenza vanishes in the bird world. Furthermore, if (0) < 1 and (0) < 1, the avian influenza vanishes in the bird and human worlds. In the case that (0) < 1 and (0) > 1, spreading of the mutant avian influenza in the human world is possible. It is also shown that if ( ) ⩾ 1 for any ⩾ 0, the avian influenza spreads in the bird world.
本文提出了一个反应扩散系统来研究禽流感。引入两个自由边界来描述禽流感的传播前沿。分别针对具有禽流感的鸟类和自由边界问题中具有变异禽流感的人类定义了基本再生数(R_0^{(1)}(t))和(R_0^{(2)}(t))。得到了这两个随时间变化的基本再生数的性质。给出了禽流感传播和消失的充分条件。结果表明，如果(R_0^{(1)}(0) \lt 1)且感染鸟类的初始数量较少，禽流感在鸟类世界中消失。此外，如果(R_0^{(1)}(0) \lt 1)且(R_0^{(2)}(0) \lt 1)，禽流感在鸟类和人类世界中消失。在(R_0^{(1)}(0) \lt 1)且(R_0^{(2)}(0) \gt 1)的情况下，变异禽流感有可能在人类世界中传播。还表明，如果对于任意(t \geqslant 0)，(R_0^{(1)}(t) \geqslant 1)，禽流感在鸟类世界中传播。
