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一类时滞病毒动力学模型的稳定性分析 被引量：2

Stability Analysis in a Basic Virus Dynamics Model with Delays
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摘要 建立并分析了一类带有两个时滞的病毒动力学模型.通过讨论,获得了有时滞情况下无病平衡点以及正平衡点的稳定性态. A basic virus dynamics model with two time delays is built and studied. The discussed results show that the stability properties of infection-free equilibrium and endemic equilibrium.
作者 郑重武 张凤琴
机构地区 运城学院应用数学系 中北大学理学院
出处 《数学的实践与认识》 CSCD 北大核心 2009年第15期108-113,共6页 Mathematics in Practice and Theory
基金 山西省自然科学基金项目(20051010) 山西省重点扶持学科项目 山西省教育厅科技开发项目(2007151)
关键词 病毒动力学模型 平衡点 时滞 virus dynamics model equilibrium time delay
分类号 Q939.4 [生物学—微生物学] O175 [理学—基础数学]
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参考文献8

  • 1Xiaowu Jiang, Xueyong Zhou, Xiangyun Shi, Xinyu Song. Analysis of stability and hopf bifurcation foir a delaydifferential equation model of HIV infection oif CD4^+ T-cells[J]. Chaos, Solitions and Fractals, 2008, 38: 447- 460.
  • 2Tsuyoshi kajiwawa, Toru Sasaki. A note on the stability analysis of patheogen-immune interaction dynamics[J]. Discrete and Continuous Dynamical System Series, 2004, B4 : 615-622.
  • 3HaiyanPang WendiWang KaifaWang.Global properties of virus dynamics with CTL immune response.西南师范大学学报：自然科学版,2005,30:796-799.
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  • 5Canabarro A A, Gera I M, Lyra M L. Periodic solutions and chaos in a non-linear model for the delayed cellular immune response[J].Physica, 2004,A342 : 234-241.
  • 6Andrei Korobeinikov. Global properties of basic virus dynamics models[J].Bulletin of Mathematical Biology, 2004,66:879-883.
  • 7Bonhoeffer S, May R M, Shaw G M, Nowak M A. Virus dynamics and drug therapy[J]. Proc Natl Acad Sci USA, 1997,94:6971- 6976.
  • 8Nowak M A, May R M. Virus Dynamics: Mathematical Principles of Immunology and Virology[M]. New York: Oxford University Press, 2000.

共引文献2

同被引文献27

  • 1Perelson A S,Nelson P W.Mathematical analysis of HIV-1 dynamics in vivo[J].SIAM Rev,1999,41(1):3-44.
  • 2Nowak M A,May R M.Virus Dynamics:Mathematial Principles of Immunology and Virology[M].Oxford:Oxford Cambridge University Press,2000.
  • 3Perelson A S,Neumann A U,Markowitz M,et al.HIV-1 dynamics in vivo:virion clearance rate,infected cell life-span,and viral generation time[J].Science,1996,271(5255):1582-1586.
  • 4Bonhoeffer S,May R M,Shaw G M,et al.Virus dynamics and drug therapy[J].Proc Natl Acad Sci USA,1997,94(13):6971-6976.
  • 5Korobeinikov A.Global properties of basic virus dynamics models[J].Bull Math Biol,2004,66(4):879-883.
  • 6Michael Y Li,SHU H Y.Global dynamics of an in-host viral model with intracellular delay[J].Bull Math Biol,2010,72(6):1492-1505.
  • 7FAN A J,WANG K F.A viral infection model with immune circadian rhythms[J].Appl Math Comput,2010,215(9):3369-3374.
  • 8HU Z X,LIU X D,WANG H,et al.Analysis of the dynamics of a delayed HIV pathogenesis model[J].J Comput Appl Mathe,2010,234(2):461-476.
  • 9ZHOU X Y,SHI X Y,ZHANG Z H,et al.Dynamical behavior of a virus dynamics model with CTL immune response[J].Appl Mathe Comput,2009,213(2):329-347.
  • 10Dalal N,Greenhalgh D,MAO X R.A stochastic model for internal HIV dynamics[J].J Math Anal Appl,2008,341(2):1084-1101.

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数学的实践与认识
2009年 第15期

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