In this paper, we investigate an age-structured HIV infection model with logistic growth for target cell. We rewrite the model as an abstract non-densely defined Cauchy problem and obtain the condition which guarantees the existence of the unique positive steady state. By linearizing the model at steady state and analysing the associated characteristic transcendental equations, we study the local asymptotic stability of the steady state. Furthermore, by using Hopf bifurcation theorem in Liu et al., we show that Hopf bifurcation occurs at the positive steady state when bifurcating parameter crosses some critical values. Finally, we perform some numerical simulations to illustrate our results.

在本文中，我们研究了具有目标细胞逻辑生长的年龄结构的HIV感染模型。我们将模型重写为抽象的非密集定义的柯西问题，并获得了保证存在唯一正稳态的条件。通过线性化稳态模型并分析相关的特征超越方程，我们研究了稳态的局部渐近稳定性。此外，通过使用Liu等人的Hopf分支定理，当分支参数超过一些临界值时，Hopf分支发生在正稳态。最后，我们执行一些数值模拟来说明我们的结果。