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一类含有非线性传染率的传染病模型的全局稳定性 被引量：11

Global Stability of an Epidemic Model with Nonlinear Incidence Rate
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摘要 讨论了一类带有非线性传染率的SIRS型传染病模型,得到了无病平衡点和地方病平衡点存在的阈值条件,借助构造Dulac函数和Liapunov函数,找到了两类平衡点全局渐近稳定的充要条件. An epidemic model with nonlinear incidence rate is investigated in this paper. The threshold of endemic equilibriums is found. By means of constructing Dulac function and Liapunov function, the necessary and sufficient condition which guarantee the global asymptotic stability of equilibriums are obtained.
作者 王拉娣
机构地区 山西财经大学应用数学系
出处 《应用数学与计算数学学报》 2004年第1期52-56,共5页 Communication on Applied Mathematics and Computation
关键词 传染病模型 阈值 平衡点 稳定性 非线性传染率 Epidemic model, threshold, equilibrium, stability
分类号 R181.8 [医药卫生—流行病学]
  • 相关文献

参考文献8

  • 1李建全,杨友社.一类带有确定隔离期的传染病模型的稳定性分析[J].空军工程大学学报（自然科学版）,2003,4(3):83-86. 被引量：14
  • 2Hethcote H.W.The mathematics of infectious disease.SIAM Reviev.,2000,42(2):599-653.
  • 3Cappasso V.Mathematical structures of epidemic systems.Springer-Verlag,Heidelberg,1993.
  • 4Busenberg S.,van den Driessche P.Analysis of a disease transmission model in a population with varying size.J.Math.Biol.,1990,28(2):257-270.
  • 5Hethcote H.W,van den Driessche P.Some epidemiological models with nonlinear incidence.J.Math.Biol.,1991,(2):271-287.
  • 6Ruan Shigui,Wang Wendi.Dynamical behavior of an epidemic model with a nonlinear incidence rate.J.Diff.Equs.,2003,188(1):135-163.
  • 7Liu Weimin,Hetchcote H.W.,Levin S.A.Dynamical behavior of epidemiological model with nonlinear incidence rates.J.Math.Biol.,1987,25(2):359-380.
  • 8Liu Weimin,Levin S.A.,Iwasa Yoh.Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models.J.Math.Biol.,1986,23(1):187-204.

二级参考文献6

  • 1Hethcote H W. Qualitative analyses of communicable disease models [ J ]. Math Biosci, 1976,28 (3) : 335 - 356.
  • 2Hethcote H W, Gao L Q. Disease transmission models with density -dependent demographics [ J]. J Math Biol, 1992,30(6) :717 -731.
  • 3Feng Z, Thieme H R. Recurrent outbreaks of childhood disease revisited: The impact of isolation [J]. Math Biosci, 1995,128(2) : 93 - 130.
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共引文献13

同被引文献65

引证文献11

二级引证文献27

应用数学与计算数学学报
2004年 第1期

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