In this paper, we formulate a mathematical model to investigate a within-host HIV dynamics under the effect of cytotoxic T lymphocytes immune response. The model incorporates two modes of transmission, virus-to-cell (VTC) and cell-to-cell (CTC). The CTC infection is due to the contact of healthy CD\(4^{+}\) T cells with (i) silent HIV-infected cells, and (ii) active HIV-infected cells. The model integrates three types of distributed time delays. We show that the model is well posed and it has three equilibria. The existence and stability of equilibria are governed by two threshold parameters. We prove the global asymptotic stability of all equilibria by utilizing Lyapunov function and LaSalle’s invariance principle. We have presented numerical simulations to illustrate the theoretical results. We have studied the effects of CTC transmission and time delays on the dynamical behavior of the system. We have shown that inclusion of time delay can significantly increase the concentration of healthy CD4\(^{+}\) T cells and reduce the concentrations of infected cells and free HIV particles. While the inclusion of CTC transmission decreases the concentration of healthy CD4\(^{+}\) T cells and increases the concentrations of infected cells and free HIV particles.

中文翻译：

---

具有无声感染的细胞间传播和CTL介导的免疫力的延迟分布的HIV感染模型的稳定性

在本文中，我们建立了一个数学模型来研究在细胞毒性T淋巴细胞免疫应答作用下宿主内HIV的动态。该模型包含两种传输模式：病毒到细胞（VTC）和细胞到细胞（CTC）。CTC感染是由于接触健康的CD \（4 ^ {+} \）具有（i）沉默的HIV感染细胞和（ii）活跃的HIV感染细胞的T细胞。该模型集成了三种类型的分布式时间延迟。我们证明该模型是正确的，并且具有三个平衡点。平衡的存在和稳定性由两个阈值参数控制。我们利用Lyapunov函数和LaSalle不变性原理证明了所有平衡点的全局渐近稳定性。我们提出了数值模拟来说明理论结果。我们已经研究了CTC传输和时间延迟对系统动态行为的影响。我们已经表明，包含时间延迟可以显着增加健康CD4 \（^ {+} \）的浓度T细胞可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的CD4 \（^ {+} \） T细胞的浓度，并增加感染细胞和游离HIV颗粒的浓度。