In this paper, we propose detailed and reasonable viral dynamics by using a multi-compartment model that incorporating the age since the infection of multiple infected cells, multiple target cells (Langerhans-cells and CD4+ T-cells), multiple viral strains (CCR5 and CXR4 HIV) and multiple infection routes (cell-to-cell and cell-to-virus). The basic reproduction number, R0, of the whole model is derived from two transmission mechanisms: one is the potential trigger from the infection routes for a single target cell and other is the joint effect of multiple viral infections for multi-target cells. Accordingly, we study the global stability of the steady states for the single target model. For the whole model, we prove that the infection-free steady state is globally asymptotically stable if R0 < 1, whereas viruses persist uniformly if R0 > 1. Numerical simulations are carried out to illustrate the theoretical results. Sensitive analyses expound the effect of model parameters on the comprehensive reproduction number. It is remarkable to find that simultaneous control of HIV infection for two target cells can effectively reduce the viral loads within-host. Finally, our work suggests that the synergetic mechanism of multi-target cells and multi-strain cannot be ignored during treatment.

中文翻译：

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两种HIV感染途径的多靶细胞和多株年龄结构模型的数学分析

在本文中，我们使用多室模型提出了详细而合理的病毒动力学，该模型结合了多个感染细胞、多个靶细胞（朗格汉斯细胞和 CD4+T 细胞）、多种病毒株（CCR5 和 CXR4 HIV）和多种感染途径（细胞对细胞和细胞对病毒）。基本再生数，R0，整个模型来源于两种传播机制：一种是感染途径对单个靶细胞的潜在触发，另一种是多种病毒感染对多靶细胞的联合作用。因此，我们研究了单目标模型稳态的全局稳定性。对于整个模型，我们证明了无感染稳态是全局渐近稳定的，如果R0 < 1，而病毒一致地持续存在，如果R0 > 1. 进行了数值模拟来说明理论结果。敏感性分析阐述了模型参数对综合再生数的影响。值得注意的是，同时控制两个靶细胞的 HIV 感染可以有效地降低宿主内的病毒载量。最后，我们的工作表明在治疗过程中不能忽视多靶细胞和多菌株的协同机制。