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摘要：为了了解病毒在人体内的感染、受制、清除等动力学过程，研究一类具有细胞感染年龄和一般饱和感染率的病毒感染动力学模型，证明当病毒的基本再生率大于1时，模型存在唯一的病毒感染稳态解。通过分析相应特征方程讨论了可行稳态解的局部稳定性，在构造Lyapunov泛函和应用LaSalle不变集原理的基础上，证明了当基本再生率小于1时，病毒未感染稳态解是全局渐近稳定的；当基本再生率大于1时，病毒感染稳态解是全局渐近稳定的。
关键词：稳定性理论；细胞感染年龄；饱和感染率；Lyapunov泛函；LaSalle不变集原理
中图分类号：O175MSC（2010）主题分类：34N05文献标志码：A
文章编号：1008-1542（2016）04-0349-08
Abstract：In order to understand the viral dynamics processes inclucding infection， duplicate， eliminate， etc. in human body， a viral infection model with infection age of cells and general saturated infection rate is investigated. It is proved that the model has a unique infected steady state when the basic reproduction ratio is greater than one unity. By analyzing the characteristic of relevant equations， the local stability of effective steady state is dislussed. By using suitable Lyapunov functional and LaSalle’s invariance principle， it is proved that when the basic reproduction ratio is less than one unity， the infection-free steady state is globally asymptotically stable； and when the basic reproduction ratio is greater than one unity， the infected steady state is globally asymptotically stable.
Keywords：stability theory； infection age of cells； saturation infection rate； Lyapunov functional； LaSalle’s invariance principle
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