| 一类HIV病毒动力学模型的全局稳定性与周期解 |
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| 引用本文： | 邵莉,李学志. 一类HIV病毒动力学模型的全局稳定性与周期解[J]. 数学的实践与认识, 2021, 0(6): 120-130 |
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| 作者姓名： | 邵莉 李学志 |
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| 作者单位： | 信阳职业技术学院数学与计算机科学学院;河南师范大学数学与信息科学学院 |
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| 摘 要： | 建立了一类较广泛的HIV感染CD4+T细胞病毒动力学模型,给出了一个感染细胞在其整个感染期内产生的病毒的平均数(基本再生数)Ro的表达式,运用Lyapunov原理和Routh-Hurwitz判据得到了该模型的未感染平衡点与感染平衡点的存在性与稳定性条件.同时也得到了模型存在轨道渐近稳定周期解和系统持续生存的条件,并通过...
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| 关 键 词： | HIV病毒动力学模型 感染平衡点 全局稳定 一致持续 周期解 |
Global Stability and Periodic Solutions for a Class of Generalized Viral Dynamical Model of HIV |
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| SHAO Li,LI Xue-zhi. Global Stability and Periodic Solutions for a Class of Generalized Viral Dynamical Model of HIV[J]. Mathematics in Practice and Theory, 2021, 0(6): 120-130 |
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| Authors: | SHAO Li LI Xue-zhi |
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| Affiliation: | (Department of Mathematics and Computer Science,Xinyang Vocational and Technical College,Xinyang 464000,China;College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China) |
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| Abstract: | This paper formulates a class of generalized viral dynamical model for HIV infection of CD4+T cells.The explicit expression of the basic reproduction number R0(it represents the average number of secondary infections caused by a single primary actively infected T cell introduced into a pool of susceptible T cells during its entire infection period) is obtained.The conditions for the existence and stability of the uninfected and infected equilibria are given.The existence conditions of an orbitally asymptotically stable periodic solution are also obtained by using Lyapunov function,additive compound matrix theory and three-dimensional competitive system theory.The theoretical results obtained in this paper are supported by numerical simulation. |
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| Keywords: | HIV viral dynamical model infected equilibrium global stability uniform persistence periodic solution |
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