In this work, we construct an age-structured HIV-1 infection model to investigate the interplay between [Formula: see text] cells and viruses. In our model, we assume that the variations in the death rate of productively infected [Formula: see text] cells and the production rate of virus in infected cells are all age-dependent, and the target cells follow logistic growth. We perform mathematical analysis and prove the persistence of the semi-flow of the system. We calculate the basic reproduction number and prove the local and global stability of the steady states. We show that if the basic reproduction number is less than one, the disease-free equilibrium is globally asymptotically stable, and if the basic reproduction number is greater than one, the infected steady state is locally asymptotically stable.

中文翻译：

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具有 LOGISTIC 靶细胞生长的年龄结构 HIV-1 感染模型的分析

在这项工作中，我们构建了一个年龄结构的 HIV-1 感染模型来研究 [公式：见文本] 细胞和病毒之间的相互作用。在我们的模型中，我们假设有效感染[公式：见正文]细胞的死亡率和感染细胞中病毒的产生率的变化都是年龄依赖性的，并且靶细胞遵循逻辑生长。我们进行数学分析并证明系统半流的持久性。我们计算基本再生数并证明稳态的局部和全局稳定性。我们表明，如果基本繁殖数小于 1，则无病平衡是全局渐近稳定的，如果基本繁殖数大于 1，则感染稳态是局部渐近稳定的。