| 一类关于HIV-1细胞到细胞传播的比率依赖时滞模型 |
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| 引用本文： | 陆志奇,袁俊丽.一类关于HIV-1细胞到细胞传播的比率依赖时滞模型[J].河南师范大学学报(自然科学版),2004,32(4):1-6. |
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| 作者姓名： | 陆志奇 袁俊丽 |
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| 作者单位： | 河南师范大学,数学与信息科学学院,河南,新乡,453007;河南师范大学,数学与信息科学学院,河南,新乡,453007 |
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| 基金项目： | 河南省自然科学基金项目资助(1999110011) |
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| 摘 要： | 研究了一类二维比率依赖模型,它描述了在组织培养皿未充分混合的情况下HIV 1的细胞到细胞的传播,并且假设感染是直接从感染细胞到健康细胞忽略了自由病毒的影响,本文研究了三类模型的稳定性:常微分方程模型的全局渐近稳定性,离散时滞微分方程模型的绝对稳定性及具有分布时滞的模型的Hopf分支.
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| 关 键 词： | HIV-1 时滞微分方程 比率依赖 功能反应 Hopf 分支 |
| 文章编号： | 1000-2367(2004)04-0001-06 |
| 修稿时间： | 2004年5月9日 |
A ratio-dependent delayed model of cell-to-cell spread of HIV-1 |
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| LU Zhi-qi,YUAN Jun-li.A ratio-dependent delayed model of cell-to-cell spread of HIV-1[J].Journal of Henan Normal University(Natural Science),2004,32(4):1-6. |
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| Authors: | LU Zhi-qi YUAN Jun-li |
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| Abstract: | A two-dimensional ratio-dependent model of cell-to-cell spread of HIV-1 in insufficiently-mixed tissue cultures is considered under the assumption that infection is spread directly from infected cells to healthy cells and neglecting the effects of free virus. The stability in all three types of models is studied. It is shown that the ODE model is globally stable and the DDE model is absolute in stability and the model with distributed delay exhibits Hopf bifurcation by using the average delay as a bifurcation parameter. The results indicate that in the insufficiently-mixed system more constrains are imposed on parameters to ensure the behaviors in well-mixed system. |
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| Keywords: | HIV-1 delay differential equations ratio-dependent Response function Hopf bifurcation |
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