留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

一类具有脉冲免疫治疗的HIV-1感染模型的动力学分析

王小娥 蔺小林 李建全

王小娥, 蔺小林, 李建全. 一类具有脉冲免疫治疗的HIV-1感染模型的动力学分析[J]. 应用数学和力学, 2019, 40(7): 728-740. doi: 10.21656/1000-0887.390334
引用本文: 王小娥, 蔺小林, 李建全. 一类具有脉冲免疫治疗的HIV-1感染模型的动力学分析[J]. 应用数学和力学, 2019, 40(7): 728-740. doi: 10.21656/1000-0887.390334
WANG Xiaoe, LIN Xiaolin, LI Jianquan. Dynamic Analysis of a Class of HIV-1 Infection Models With Pulsed Immunotherapy[J]. Applied Mathematics and Mechanics, 2019, 40(7): 728-740. doi: 10.21656/1000-0887.390334
Citation: WANG Xiaoe, LIN Xiaolin, LI Jianquan. Dynamic Analysis of a Class of HIV-1 Infection Models With Pulsed Immunotherapy[J]. Applied Mathematics and Mechanics, 2019, 40(7): 728-740. doi: 10.21656/1000-0887.390334

一类具有脉冲免疫治疗的HIV-1感染模型的动力学分析

doi: 10.21656/1000-0887.390334
基金项目: 国家自然科学基金(11371031;11371369)
详细信息
    作者简介:

    王小娥(1993—),女,硕士生(E-mail: 1255013427@qq.com);李建全(1965—),男,博士(通讯作者. E-mail: jianq_li@263.net).

  • 中图分类号: O29

Dynamic Analysis of a Class of HIV-1 Infection Models With Pulsed Immunotherapy

Funds: The National Natural Science Foundation of China(11371031;11371369)
  • 摘要: 该文基于一类HIV-1感染免疫治疗模型,研究了一类具有脉冲免疫治疗的HIV-1感染模型.借助脉冲微分方程理论,研究了脉冲免疫治疗模型解的非负性和一致有界性.利用Floquet乘子理论和微分方程的比较定理,推导出脉冲免疫模型无感染周期解局部和全局渐近稳定以及HIV-1一致持续的阈值条件.通过数值模拟,比较了3种不同治疗方案的治疗效果,验证了脉冲免疫治疗的有效性.数值模拟结果表明,当药物输入量足够大或服药间隔适当短时,从理论上可以有效控制甚至根除病毒.
  • [1] AIDS, Information on HIV[EB/OL]. [2018-11-29]. https://aidsinfo.nih.gov/clinical-trials.
    [2] KIRSCHNER D E, WEBB G F. Immunotherapy of HIV-1 infection[J]. Journal of Biological Systems,1998,6(1): 71-83.
    [3] PERELSON A S, NELSON P W. Mathematical analysis of HIV-1 dynamics in vivo[J]. Society for Industrial and Applied Mathematics,1999,41(1): 3-44.
    [4] CALLAWAY D S, PERELSON A S. HIV-1 infection and low steady state viral loads[J]. Bulletin of Mathematical Biology,2002,64(1): 29-64.
    [5] LEENHEER P D, SMITH H L. Virus dynamics: a global analysis[J]. SIAM Journal on Applied Mathematics,2003,63(4): 1313-1327.
    [6] HUANG Y X, ROSENKRANZ S L, WU H L. Modeling HIV dynamics and antiviral response with consideration of time-varying drug exposures, adherence and phenotypic sensitivity[J]. Mathematical Biosciences,2003,184(2): 165-186.
    [7] SMITH R J, WAHL L M. Distinct effects of protease and reverse transcriptase inhibition in an immunological model of HIV-1 infection with impulsive drug effects[J]. Bulletin of Mathematical Biology,2004,66(5): 1259-1283.
    [8] SMITH R J, WAHL L M. Drug resistance in an immunological model of HIV-1 infection with impulsive drug effects[J]. Bulletin of Mathematical Biology,2005,67(4): 783-813.
    [9] GAO T, WANG W D, LIU X N. Mathematical analysis of an HIV model with impulsive antiretroviral drug doses[J].Mathematics and Computers in Simulation,2012, 82(4): 653-665.
    [10] MIRON R E, SMITH R J. Resistance to protease inhibitors in a model of HIV-1 infection with impulsive drug effects[J]. Bulletin of Mathematical Biology,2014,76(1): 59-97.
    [11] 宋保军, 娄洁, 文清芝. 使用T-20治疗HIV-1患者的不同策略的数学建模与研究[J]. 应用数学和力学, 2011,32(4): 400-416.(SONG Baojun, LOU Jie, WEN Qingzhi. Modelling two different therapy strategies for drug T-20 on HIV-1 patients[J]. Applied Mathematics and Mechanics,2011,32(4): 400-416.(in Chinese))
    [12] 韩溢. 具有脉冲免疫因子的HIV模型的稳定性研究[J]. 重庆工商大学学报(自然科学版), 2013, 30(3): 77-82.(HAN Yi. Research on stability for an HIV model with impulsive releasing immune factor[J]. Journal of Chongqing Technology and Business University(Natural Science ), 2013,30(3): 77-82.(in Chinese))
    [13] ROY P K, CHATTERJEE A N, LI X Z. The effect of vaccination to dendritic cell and immune cell interaction in HIV disease progression[J]. International Journal of Biomathematics,2016,9(1): 1-20.
    [14] CHATTERJEE A N, ROY P K. Anti-viral drug treatment along with immune activator IL-2: a control-based mathematical approach for HIV infection[J]. International Journal of Control,2012, 85(2): 220-237.
    [15] JOLY M, ODLOAK D. Modeling interleukin-2-based immunotherapy in AIDS pathogenesis[J]. Journal of Theoretical Biology,2013,335(4): 57-78.
    [16] ABRAMS D, LEVY Y, LOSSO M H. Interleukin-2 therapy in patients with HIV infection[J]. New England Journal of Medicine,2009,361(16): 1548-1559.
    [17] BELL C J M, SUN Y L, NOWAK U M, et al. Sustained in vivo signaling by long-lived IL-2 induces prolonged increases of regulatory T cells[J]. Journal of Autoimmunity,2015,56: 66-80.
    [18] READ S W, LEMPICKI R A, MASCIO M D, et al. CD4 T cell survival after intermittent interleukin-2 therapy is predictive of an increase in the CD4 T cell count of HIV-infected patients[J]. The Journal of Infectious Diseases,2008,198(6): 843-850.
    [19] 胡晓虎, 唐三一. 血管外给药的非线性房室模型解的逼近[J]. 应用数学和力学, 2014,35(9): 1033-1045.(HU Xiaohu, TANG Sanyi. Approximate solutions to the nonlinear compartmental model for extravascular administration[J]. Applied Mathematics and Mechanics,35(9): 1033-1045.(in Chinese))
    [20] KIRSCHNER D E, WEBB G F. A mathematical model of combined drug therapy of HIV infection[J]. Journal of Theoretical Medicine,2014,1(1):25-34.
    [21] 宋新宇, 郭红建, 师向云. 脉冲微分方程理论及其应用[M]. 北京: 科学出版社, 2011.(SONG Xinyu, GUO Hongjian, SHI Xiangyun. Impulsive Differential Equation Theory and Its Application [M]. Beijing: Science Press, 2011.(in Chinese))
    [22] 陆启韶. 常微分方程的定性方法和分叉[M]. 北京: 北京航空航天大学出版社, 1989.(LU Qishao. Qualitative Methods and Bifurcations of Ordinary Differential Equations [M]. Beijing: Beihang University Press, 1989.(in Chinese))
    [23] FONDA A. Uniformly persistent semidynamical systems[J]. Proceedings of the American Mathematical Society,1988,104(1): 111-116.
    [24] 白振国. 周期传染病模型的基本再生数[J]. 工程数学学报, 2013,30(2): 175-183.(BAI Zhenguo. Basic reproduction number of periodic epidemic models[J]. Chinese Journal of Engineering Mathematics,2013,30(2): 175-183.(in Chinese))
  • 加载中
计量
  • 文章访问数:  995
  • HTML全文浏览量:  198
  • PDF下载量:  381
  • 被引次数: 0
出版历程
  • 收稿日期:  2018-11-29
  • 修回日期:  2019-05-06
  • 刊出日期:  2019-07-01

目录

    /

    返回文章
    返回