We propose and analyse an age-structured model for within-host HIV virus dynamics which is incorporated with both virus-to-cell and cell-to-cell infection routes, and proliferations of both uninfected and infected cells in the form of logistic growth. The model turns out to be a hybrid system with two differential-integral equations and one first-order partial differential equation. We perform some rigorous analyses for the considered model. Among the interesting dynamical behaviours of the model is the occurrence of backward bifurcation in terms of the basic reproduction number R0 at R0 = 1, which raises new challenges for effective infection control. We also discuss the cause of such a backward bifurcation, based on our analytical results.

中文翻译：

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具有增殖和两种感染模式的年龄结构 HIV 宿主模型分析

我们提出并分析了一个年龄结构的宿主内 HIV 病毒动力学模型，该模型与病毒到细胞和细胞到细胞的感染途径以及未感染和感染细胞以逻辑增长形式的增殖相结合。该模型结果是一个具有两个微分积分方程和一个一阶偏微分方程的混合系统。我们对所考虑的模型进行了一些严格的分析。该模型有趣的动力学行为之一是在基本再生数方面发生了后向分叉R0在R0= 1，这对有效控制感染提出了新的挑战。根据我们的分析结果，我们还讨论了这种向后分叉的原因。