| 一类具有时滞和治愈率的HIV病理模型的稳定性 |
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| 引用本文： | 刘祥东,王辉,胡志兴,马万彪. 一类具有时滞和治愈率的HIV病理模型的稳定性[J]. 生物数学学报, 2011, 0(1): 108-116 |
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| 作者姓名： | 刘祥东 王辉 胡志兴 马万彪 |
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| 作者单位： | [1]北京科技大学经济管理学院,北京100083 [2]北京科技大学应用数力系,北京100083 |
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| 基金项目： | 国家自然科学基金资助（11071013） |
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| 摘 要： | 研究一类具有饱和感染率、治愈率和细胞内时滞的HIV病理模型.首先分析平衡态的存在性与稳定性,然后给出染病平衡态对于任意时滞保持稳定（不稳定）的充分条件,并利用Nyquist准则度量染病平衡点保持稳定的时滞长度.
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| 关 键 词： | 稳定性 HIV感染 CD4~＋T细胞 治愈率 饱和感染率 |
Stability of an HIV Pathogenesis Model with Delay and Cure Rate |
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| LIU Xiang-dong,WANG Hui,HU Zhi-xing,MA Wan-biao. Stability of an HIV Pathogenesis Model with Delay and Cure Rate[J]. Journal of Biomathematics, 2011, 0(1): 108-116 |
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| Authors: | LIU Xiang-dong WANG Hui HU Zhi-xing MA Wan-biao |
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| Affiliation: | 1 School of Economics and Management,University of Science and Technology Beijing,Beijing 100083 China) (2 Department of Applied Mathematics and Mechanics,University of Science and Technology Beijing,Beijing 100083 China) |
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| Abstract: | An HIV pathogenesis model with saturated infection rate,intracellular delay and cure rate is analyzed.We first analyze the existence and stability of equilibria,and then give sufficient conditions ensure that the infected steady state keeps stable（unstable）for all delay. Furthermore,we apply the Nyquist criterion to estimate the length of delay for which stability continues to hold. |
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| Keywords: | Stability HIV infection CD4^＋ T cells Cure rate Saturated infection rate Delay |
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