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一类具有感染时滞的HIV模型的稳定性分析 被引量：9

Stability Analysis of an HIV Model with Infection Delay
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摘要 在基本病毒动力学模型的基础上,建立了一个具有HollingⅡ型感染率且带有时滞的HIV模型.通过稳定性分析,讨论了模型无病平衡点以及正平衡点的稳定性态.最后借助Matlab对模型进行了数值模拟. In this paper, an HIV model with Holling type Ⅱ infection response rate and time delays is built based on the basic virus dynamics model. By analyzing, the stability properties of infection-free equilibrium and endemic equilibrium is discussed. Last the numerical simulations is given.
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 2010年第13期247-252,共6页 Mathematics in Practice and Theory
基金 山西省自然科学基金项目(2009011005-3) 山西省重点扶持学科项目
关键词 病毒动力学模型 平衡点 时滞 数值模拟 virus dynamics model equilibrium time delay numerical simulations
分类号 O242.1 [理学—计算数学]
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参考文献7

  • 1Bonhoeffer S, May R M, Shaw G M and Nowak M A. Virus dynamics and drug therapy[J]. Proc Natl Acad SciUSA, 1997(94): 6971-6976.
  • 2Nowak M A and May R M. Virus Dynamics:Mathematical Principles of Immunology and Virology[M]. New York: Oxford University Press, 2000.
  • 3Andrei Korobeinikov, Global properties of basic virus dynamics models[J]. Bulletin of Mathematical Biology, 2004(66): 879-883.
  • 4Wang K, Wen W, Pang H, Liu X. Complex dynamic behavior in a viral model with delayed immune response[J]. Physica D, 2007(226): 197-208.
  • 5Canabarro A A, Gdra I M, Lyra M L. Periodic solutions and chaos in a non-linear model for the delayed cellular immune response[J]. Physica A, 2004(342): 234-241.
  • 6Nelson P W, Perelson A S. Mathematical analysis of a delay differential equation models of HIV-1 infection[J]. Math Biosci, 2002(179): 74-79.
  • 7Gang Huang, Wanbiao Ma, Yasuhiro Takeuchi. Global properties of virus dynamics model with Beddington-DeAngelis functional response[J]. Applied Mathematics Letters, in press.

同被引文献31

  • 1JIANG X W, ZHOU X Y, SHI X Y, et al. Analysis of stability and Hopf bifurcation for a delay- differential equation model of HIV infection of CD4^+ T-cells[J]. Chaos, Solitons and Fractals, 2008, 38(2): 447-460.
  • 2ZHU H Y, LUO Y, CHEN M L. Stability and ttopf bifurcation of a HIV infection model with CTL- response delay[J]. Computers and Mathematics with Applications,2011, 62(8): 3091-3102.
  • 3TIAN X H, XU R. Global stability and Hopf bifurcation of an HIV-1 infection model with saturation incidence and delayed CTL immune response[J]. Applied Mathematics and Computation,2014, 237(4): 146-154.
  • 4Culshaw R V, RUAN S G. A delay differential equation model of HIV infection of CD4^+ T-cells[J]. Math Biosci, 2000, 165(3): 27-39.
  • 5SONG Y L, WEI J J. Bifurcation analysis for Chen's system with delayed feedback and its application to control of chaos[J]. Chaos Solitons and Fractals, 2004, 22(1):75-91.
  • 6Hale J K, Lunel S V. Introduction to Functional Differential Equation[M]. New York: Springer-Verlag, 1993.
  • 7Nowak M A, Bonhoeffer S, Hill A M, et al. Viral dynamics in hepatitis B virus infection [ J ]. Proc. Natl. Acad. Sci USA, 1996,93 (9) : 4398 - 4402.
  • 8A M Elaiw, S A Azoz. Global properties of a class of HIV infection models with Beddington- DeAngelis functional response [ J ]. Mathe- matical Metheods in the Applied Sciences, 2013,36 (4) : 779 - 794.
  • 9A Korobeinikov. Global properties of basic virus dynamics models [ J ]. Bulletin of Mathematical Biology,2014,66 (4) : 879 - 883.
  • 10CUIFANG L V,LI Honghuang,ZHAO Huiyuan. Global stability for an HIV-1 infection model with Bedding- ton-DeAngelis incidence rate and CTL immune response[J].Commun Nonlinear Sci Numer Simulat2014,19(1 ):121-127.

引证文献9

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数学的实践与认识
2010年 第13期

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