发表机构
Volgograd State University（伏尔加格勒国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究构建并分析了一个包含免疫应答与抗逆转录病毒治疗的宿主内HIV动力学ODE模型，推导了基本再生数与抑制阈值，并通过数值模拟验证了治疗对病毒载量和CD4$^+$ T细胞恢复的作用，为临床数据校准提供了基础。
AI 中文摘要
我们开发并分析了一个宿主内HIV动力学的机制性常微分方程（ODE）模型，该模型包含未感染的CD4$^+$ T细胞、潜伏感染细胞、产毒性感染细胞、游离病毒颗粒以及细胞毒性免疫效应细胞。抗逆转录病毒治疗通过两个随时间变化的疗效函数来描述，这两个函数分别减少新感染和病毒颗粒的产生。我们证明了模型的解保持非负且有界，确定了无感染平衡点和地方性平衡点，并推导了基本再生数以及无感染状态的局部稳定性条件。我们还获得了依赖于治疗的抑制阈值，以及当治疗疗效下降时该阈值被跨越的时间的解析估计。数值模拟考虑了未治疗感染、ART启动、疗效的周期性变化以及治疗效果的逐渐丧失。在没有治疗的情况下，模型趋于持续感染的状态。ART降低病毒载量并促进CD4$^+$ T细胞群体的恢复，而在所考虑的参数集下，潜伏库持续存在。治疗疗效的周期性变化产生持续的受迫振荡。这些结果将解析阈值条件与模型依赖于治疗的动态联系起来，并为未来的校准、敏感性分析、不确定性量化以及基于临床数据的扩展提供了基础。
英文摘要
We develop and analyse a mechanistic ODE model of within-host HIV dynamics that includes uninfected CD4$^+$ T cells, latently and productively infected cells, free virions, and cytotoxic immune effectors. Antiretroviral therapy is described by two time-dependent efficacy functions that separately reduce new infections and virion production. We show that solutions remain non-negative and bounded, identify the infection-free and endemic equilibria, and derive the basic reproduction number together with the local stability condition for the infection-free state. We also obtain treatment-dependent suppression thresholds and an analytical estimate of when this threshold is crossed as treatment efficacy declines. Numerical simulations consider untreated infection, ART initiation, periodic variation in efficacy, and progressive loss of treatment effect. Without therapy, the model approaches a state of persistent infection. ART reduces viral load and promotes recovery of the CD4$^+$ T-cell population, while the latent reservoir persists under the parameter set considered. Periodic changes in treatment efficacy produce sustained forced oscillations. These results connect the analytical threshold conditions with the treatment-dependent dynamics of the model and provide a basis for future calibration, sensitivity analysis, uncertainty quantification, and extensions informed by clinical data.
