The activation status can dictate the fate of an HIV-infected CD4+ T cell. Infected cells with a low level of activation remain latent and do not produce virus, while cells with a higher level of activation are more productive and thus likely to transfer more virions to uninfected cells during cell-to-cell transmission. How the activation status of infected cells affects HIV dynamics under antiretroviral therapy remains unclear. We develop a new mathematical model that structures the population of infected cells continuously according to their activation status. The effectiveness of antiretroviral drugs in blocking cell-to-cell viral transmission decreases as the level of activation of infected cells increases because the more virions are transferred from infected to uninfected cells during cell-to-cell transmission, the less effectively the treatment is able to inhibit the transmission. The basic reproduction number \(R_{0}\) of the model is shown to determine the existence and stability of the equilibria. Using the principal spectral theory and comparison principle, we show that the infection-free equilibrium is locally and globally asymptotically stable when \(R_{0}\) is less than one. By constructing Lyapunov functional, we prove that the infected equilibrium is globally asymptotically stable when \(R_{0}\) is greater than one. Numerical investigation shows that even when treatment can completely block cell-free virus infection, virus can still persist due to cell-to-cell transmission. The random switch between infected cells with different activation levels can also contribute to the replenishment of the latent reservoir, which is considered as a major barrier to viral eradication. This study provides a new modeling framework to study the observations, such as the low viral load persistence, extremely slow decay of latently infected cells and transient viral load measurements above the detection limit, in HIV-infected patients during suppressive antiretroviral therapy.

激活状态可以决定 HIV 感染的 CD4+ T 细胞的命运。具有低激活水平的受感染细胞保持潜伏并且不产生病毒，而具有更高激活水平的细胞具有更高的生产力，因此可能在细胞间传播过程中将更多的病毒粒子转移到未感染的细胞中。受感染细胞的激活状态如何影响抗逆转录病毒治疗下的 HIV 动力学仍不清楚。我们开发了一种新的数学模型，该模型根据其激活状态连续构建受感染细胞的群体。抗逆转录病毒药物阻断细胞间病毒传播的有效性随着受感染细胞激活水平的增加而降低，因为在细胞间传播过程中，更多的病毒粒子从感染细胞转移到未感染细胞，治疗能够抑制传播的效果越差。基本再生数显示模型的\(R_{0}\)以确定平衡的存在性和稳定性。使用主谱理论和比较原理，我们表明当\(R_{0}\)小于 1 时，无感染平衡是局部和全局渐近稳定的。通过构造 Lyapunov 泛函，我们证明了当\(R_{0}\)时，感染平衡是全局渐近稳定的大于一。数值研究表明，即使治疗可以完全阻断无细胞病毒感染，由于细胞间传播，病毒仍然可以持续存在。具有不同激活水平的感染细胞之间的随机切换也有助于补充潜在的水库，这被认为是消灭病毒的主要障碍。这项研究提供了一个新的建模框架来研究在抑制性抗逆转录病毒治疗期间 HIV 感染患者的观察结果，例如低病毒载量持续性、潜伏感染细胞的极慢衰减和超过检测限的瞬时病毒载量测量值。