This paper investigates an adaptive immunity HIV infection model with three types of distributed time delays. The model describes the interaction between healthy CD4⁺T cells, silent infected cells, active infected cells, free HIV particles, Cytotoxic T lymphocytes (CTLs) and antibodies. The healthy CD4⁺T cells can be infected when they contacted by free HIV particles or silent infected cells or active infected cells. The incidence rates of the healthy CD4⁺T cells with free HIV particles, silent infected cells, and active infected cells are given by general functions. Moreover, the production/proliferation and removal/death rates of the virus and cells are represented by general functions. The model is an improvement of the existing HIV infection models which have neglected the infection due to the incidence between the silent infected cells and healthy CD4⁺T cells. We show that the model is well posed and it has five equilibria and their existence are governed by five threshold parameters. Under a set of conditions on the general functions and the threshold parameters, we have proven the global asymptotic stability of all equilibria by using Lyapunov method. We have illustrated the theoretical results via numerical simulations. We have studied the effect of cell-to-cell (CTC) transmission and time delays on the dynamical behavior of the system. We have shown that the inclusion of time delay can significantly increase the concentration of the healthy CD4⁺ T cells and reduce the concentrations of the infected cells and free HIV particles. While the inclusion of CTC transmission decreases the concentration of the healthy CD4⁺ T cells and increases the concentrations of the infected cells and free HIV particles.

中文翻译：

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具有主动和静默细胞间传播的适应性免疫力延迟性HIV感染模型的稳定性

本文研究了一种具有三种分布式时延的自适应免疫HIV感染模型。该模型描述了健康的CD4 ⁺ T细胞，沉默感染细胞，活性感染细胞，游离HIV颗粒，细胞毒性T淋巴细胞（CTL）和抗体之间的相互作用。健康的CD4 ⁺ T细胞在接触游离的HIV颗粒，沉默感染的细胞或活动感染的细胞后即可被感染。健康CD4 ⁺的发生率具有游离HIV颗粒的T细胞，沉默感染的细胞和活性感染的细胞由一般功能提供。而且，病毒和细胞的产生/增殖和去除/死亡速率由一般功能表示。该模型是对现有HIV感染模型的改进，该模型已忽略了由于无声感染细胞与健康CD4 ⁺T细胞。我们证明了该模型的正确性，它具有五个平衡点，它们的存在由五个阈值参数控制。在一般函数和阈值参数的一组条件下，我们使用Lyapunov方法证明了所有平衡点的全局渐近稳定性。我们已经通过数值模拟说明了理论结果。我们已经研究了单元间（CTC）传输和时间延迟对系统动态行为的影响。我们已经表明，包括时间延迟可以显着增加健康的CD4 ⁺ T细胞的浓度，并降低感染细胞和游离HIV颗粒的浓度。虽然包含四氯化碳传播会降低健康CD4 ⁺的浓度 T细胞并增加了感染细胞和游离HIV颗粒的浓度。