We propose and analyze a virus-to-cell and cell-to-cell infections HIV model that includes intracellular time delay and infection-age structure, where infection-age-specific conversion function is considered as the piecewise function related to infection period between initial infection and the formation of productively infected cells. Applying the theory of integrated semigroup and the Hopf bifurcation theory for semilinear equations with non-dense domain, we concern the Hopf bifurcation of the model. A non-trivial periodic solution bifurcates from the positive equilibrium, when bifurcation parameter passes through some critical values. The numerical results verify our theoretical conclusion and further demonstrate that intracellular time delay has a greater impact on the model, but the impact of infection period on the model is hardly obvious. Additionally, the sensitivity of the threshold parameter is also carried out by employing the Latin hyper-cube sampling (LHS) method and partial rank correlation coefficient (PRCC) techniques.

我们提出并分析了一种病毒对细胞和细胞间感染的HIV模型，该模型包括细胞内时间延迟和感染年龄结构，其中感染年龄特异性转化功能被认为是与初始感染之间的感染期有关的分段功能。感染和生产性感染细胞的形成。将积分半群理论和Hopf分支理论应用于具有稠密域的半线性方程组，我们关注模型的Hopf分支。当分叉参数通过一些临界值时，非平凡的周期解从正平衡中分叉。数值结果验证了我们的理论结论，并进一步证明细胞内时间延迟对模型的影响更大，但是感染期对模型的影响几乎不明显。