两个艾滋病相关的癌症动力学模型研究(英文) 被引量：2

Two Differential Equation Models About AIDS-related Cancer

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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。 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.

作者娄洁王晓微娄梅枝

机构地区上海大学理学院数学系河南公安高等专科学校

出处《工程数学学报》 CSCD 北大核心 2008年第5期779-787,共9页 Chinese Journal of Engineering Mathematics

基金 NNSF of China (10701053 10531030) The item of Shanghai Municipal EducationCommission (06AZ086)

关键词 HIV-1感染癌症 ODE模型 DDE模型 HIV-1 infection cancer ODE model DDE model

分类号 O175.7 [理学—基础数学]

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