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基于禽流感的一类模型建立与性态研究 被引量:5

The Study of Dynamic Behaviors for a Model on Avian Influenza
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摘要 禽流感是当前流行的一类复杂的疾病,它可以由动物传染给人类,因此为了研究它的流行性态和防治方案,建立了一类带有预防接种的传染病动力学模型.计算了基本再生数R0,通过分析这个模型,我们得到了如果当R0<1时,只存在一个无病平衡点,疾病消除;当R0>1时,存在惟一的地方病平衡点,即疾病流行.并且构造了适当的Liapunov函数证明了该模型的无病平衡点和地方病平衡点的全局稳定性. As a complex epidemic today, avian influenza can be transmitted to human by animals. In order to study its epidemiology feature and find effective control methods for preventing its transmission, we establish a epidemic model with vaccination. The basic reproduction number R0 is obtained. If R0 〈 1, there exist a unique disease-free equilibrium, which means the disease would die out finally. If R0 〉 1, then there exist unique endemic equilibrium which means the disease would become epidemic. We prove the global stability of the disease's disease-free equilibrium and endemic equilibrium using certain Liapunov function method.
作者 白京 李桂花
机构地区 中北大学数学系
出处 《数学的实践与认识》 CSCD 北大核心 2013年第18期287-291,共5页 Mathematics in Practice and Theory
基金 国家自然科学基金(11201434) 山西省回国留学人员科研资助项目(2013-087)
关键词 禽流感 平衡点 LIAPUNOV函数 稳定性 avian influenza equilibrial liapunov function stability
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参考文献8

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同被引文献30

  • 1胡新利.潜伏期具有传染力的传染病模型分析[J].西安工程大学学报,2012,26(6):801-806. 被引量:5
  • 2李建全,马知恩.两类带有确定潜伏期的SEIS传染病模型的分析[J].系统科学与数学,2006,26(2):228-236. 被引量:12
  • 3闫萍,吴昭英.具潜伏期的无免疫型传染病动力学的微分模型[J].生物数学学报,2006,21(1):47-56. 被引量:22
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  • 5国家卫生计生委疾病预防控制局.国家卫生计生委关于调整部分法定传染病病种管理工作的通知[EB].http://www.nhfpc.gov.cn/jkj/s3577/201311/f6ee56b5508a4295a8d552ca5f0f5edd.shtml.
  • 6中国疾病预防控制中心.世卫组织关于H7N9禽流感常见问题的回答[EB].http://www.chinacdc.cn/jkzt/crb/rgrgzbxqlg-5295/rgrqlgyq/201304/t20130405-79495.htm.
  • 7Shingo I,Yasuhiro T,Liu XN.Avian-human influenza epidemic model[J].Mathematical Biosciences,2007,27:1-25.
  • 8Shingo I,Yasuhiro T,Andrei K,et al.Prevention of avian influenza epidemic:What policy should we choose?[J].Journal of Theoretical Biology,2008,252:732-741.
  • 9Shingo I,Yasuhiro T,The vaccination program against avian influenza:A mathematical approach[J].数理解析研究所讲究录,2008,1582:87-101.
  • 10Vanden DP,Watmough J.Reproduction numbers and sub-threshold endemic equilibria for compartmentsl models of disease transmission[J].Mathematical Biosciences,2002,180:29-48.

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