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两个艾滋病相关的癌症动力学模型研究
  • ISSN号：1005-3085
  • 期刊名称：《工程数学学报》
  • 时间：0
  • 分类：O175.7[理学—数学;理学—基础数学]
  • 作者机构：[1]上海大学理学院数学系,上海200444, [2]河南公安高等专科学校,郑州450002
  • 相关基金：NNSF of China （10701053; 10531030）; The item of Shanghai Municipal Education Commission （06AZ086）.
作者： 娄洁[1], 王晓微[1], 娄梅枝[2]
关键词： HIV-1感染, 癌症, ODE模型, DDE模型, HIV-1 infection, cancer, ODE model, DDE model
中文摘要：

考虑到癌症在HIV感染者中的高发特点,本文建立两个艾滋病与癌症相结合的HIV-1动力学模型：一个ODE模型;一个DDE模型。该类系统有四个平衡态。我们讨论了在不同的免疫状况下这些平衡态的存在性、稳定性以及其生物学意义。在DDE模型中,我们讨论了正平衡态Hopf分支的存在条件。文中结果与一些医学临床结果及试验室观察相吻合。

英文摘要：

Considering the fact that cancer remains a significant burden in HIV-infected individuals,studied in this paper are two HIV-1 dynamical models （one ODE model and one DDE model） incorporating the AIDS-related cancer cells. The two models consist of four com-ponents, cancer cells, healthy CD4＋ T lymphocytes, infected CD4＋ T lymphocytes and free HIV-1 virus. The systems can have four steady states. We discuss the existence, stabil-ity properties and the biological meanings of these steady states under different situations of the immune system and different virulence of HIV. For the DDE model, we also find conditions for the Hopf bifurcation of the positive steady state. Our results are consistent with some clinical and experimental observations.

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期刊信息
  • 《工程数学学报》
  • 北大核心期刊（2011版）
  • 主管单位:教育部
  • 主办单位:西安交通大学
  • 主编：李大潜
  • 地址：西宁市咸宁西路28号西安交通大学数学与统计学院
  • 邮编：710049
  • 邮箱：jgsx@mail.xjtu.edu.cn
  • 电话：029-82667877
  • 国际标准刊号：ISSN：1005-3085
  • 国内统一刊号：ISSN：61-1269/O1
  • 邮发代号:
  • 获奖情况:
  • 《中文核心期刊要目总览》核心期刊,《中国科学引文数据库》核心期刊,《中国数学文摘》核心期刊,陕西省优秀科技期刊
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,荷兰文摘与引文数据库,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:6741