中文摘要：

本文主要研究具有时滞和毒性淋巴细胞（CTL）免疫反应的HIV感染模型的动力学行为.分别引入两类时滞：一类描述新感染的细胞开始产生病毒所需的时间,另一类是控制病毒复制的免疫反应出现所需的时间.通过分析时滞对平衡点稳定性的影响,建立了系统的无病平衡点P0,地方病平衡点P1的局部渐近稳定性.并且证明了在一定条件下,在地方病平衡点附近时滞可以诱导产生Hopf分支.

英文摘要：

The dynamic behaviors of a new delayed human ir~nunodeficiency virus （HIV） infection model with Cytotoxic Lymphocyte （CTL） immune response are studied in our paper. Two delays are incorporated into the model, which describe the time needed for newly infected cells to begin producing viruses and the time needed for the adaptive response to emerge to control viral replication. The effects of time delays on stabilities of the equilibria of our model have been established and some sufficient conditions for local asymptotic stabilities of the disease-free equilibrium P0, endemic equilibrium P1. We also show that the delays can induce Hopf bifurcation around endemic equilibrium P1 under some conditions hold.