一类具有时滞的HIV感染模型的动力学性态

研究一类具有胞内时滞和饱和发生率的HIV感染动力学模型，通过计算得到了病毒感染的基本再生率。进而，通过分析特征方程根的分布，讨论了系统可行平衡点的局部渐近稳定性。根据构造的Lyapunov泛函，证明了当基本再生率小于1时，病毒未感染平衡点是全局渐近稳定的。利用无穷维动力系统的持续生存理论证明了当基本再生率大于1时，系统是一致持续生存的。最后，采用比较原理和单调迭代技巧，给出了病毒感染平衡点全局吸引的充分条件。

Dynamic Behavior of an HIV Infection Model with Intracellular Delay

An HIV infection dynamics model with intracellular delay is studied. The basic reproduction ratio is obtained by calculation. By analyzing the distribution of roots of the corresponding characteristic equations, the local stability of each of feasible equilibria is established. By constructing the suitable Lyapunov functional, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable. From the persistence theory of infinite dimensional dynamic system, it shows that if the basic reproduction ratio is greater than unity, the system is uniformly persistent. According to the iteration technique and comparision arguments, the sufficient conditions are obtained for the global attractivity of the chronic infection equilibrium.