摘要
禽流感是一种能够感染人畜的传染性疾病,野生鸟类在禽流感的传播与流行中起到不可忽视的作用.建立常微分方程模型来刻画禽流感在人类及禽类中的动态传播规律.模型包含患病鸟类的迁入,并且禽类和人类数量是可变的.通过构造适当的Liapunov函数及LaSalle不变性原理证明了平衡点的局部及全局稳定性.在病鸟类迁入率不为零时,利用Poincare-Bendixson定理证明了地方病平衡点的全局渐进稳定性.还对模型进行了仿真及敏感性分析,讨论了含患病鸟类的迁入对禽流感流行的影响以及控制禽流感应采取的措施,为控制禽流感疫情提供理论基础.
Avian influenza is an infectious disease that can infect human and animals. Wild birds play an important role in the spread and prevalence of avian influenza. In the paper, an ordinary differential equation model is established to characterize the dynamic propagation of avian influenza in humans and birds. The model contains the influx of diseased birds, and the variable of birds and humans. The local and global stability of the equilibrium point is proved by constructing appropriate Liapunov function and LaSalle invariance principle. In the case of sick bird migration rate is not zero, the global asymptotic stability of the equilibrium point of endemic disease is proved by Poincare-Bendixson theorem. In this paper, the simulation and sensitivity analysis of the model were carried out. The influencing factors of avian influenza and the measures to control avian influenza were discussed, which provided the theoretical basis for the control of avian influenza.
作者
任明
高俊莲
徐向阳
REN Ming GAO Jun-lian XU Xiang-yang(Management School, China University of Mining and Technology（Beijing）, Beijing 100083, China College of Geoscience and Surveying Engineering, China University of Mining and Technology（Beijing）, Beijing 100083, China Center for Resources and Environmental Policy Research, China University of Mining and Technology （Beijing）, Beijing 100083, China)
出处
《数学的实践与认识》
北大核心
2017年第18期310-320,共11页
Mathematics in Practice and Theory
关键词
禽流感
迁徙
全局稳定
Avian influenza
migration
global stability
