研究了一类年龄结构的CD4~+T-细胞模型.得到了控制HIV病毒扩散的阈值R_0.当R_0<1时,无病平衡点全局渐近稳定,病毒在人体内消除;当R_0>1,且-r+(2αrT~*)/(T_(max))>0,地方病平衡点局部渐近稳定,病毒在人体内繁殖;当R_0>1,且-r+(2αrT~*)/(T_(max))<0,系统由感染年龄而产生的复杂动力学行为,如Hopf分支,四周期解及混沌等.最后对模型的复杂动力学行为进行了数值模拟. A class of CD4 ~ + T-cell model of age structure was studied, and the threshold R_0 for controlling the spread of HIV was obtained.When R_0 <1, the disease-free equilibrium was globally asymptotically stable and eliminated in the human body. When R_0> 1 , And -r + (2αrT ~ *) / (T_ (max))> 0, the endemic balance was locally asymptotically stable and the virus multiplied in the human body. When R_0> 1 and -r + max)) <0, complex dynamical behavior of the system caused by age of infection, such as Hopf bifurcation, quaternary periodic solution, chaos, etc. Finally, the complex dynamics of the model are numerically simulated.