AI 中文总结
研究将HIV病毒反弹建模为随机首次通过问题，把成功重新激活事件视为具有时间依赖性强度过程，给出病毒载量是泊松散粒噪声过程，推导不同激活情况下反弹时间分布及似然函数。
AI 中文摘要
在我们早期工作中，将潜伏细胞重新激活视为抗逆转录病毒疗法（ART）洗脱、免疫调节和治疗扰动期间的泊松驱动过程，对HIV反弹的随机启动进行建模。但分析性治疗中断（ATI）研究中观察到的终点不是首次成功重新激活的隐藏时间，而是血浆病毒超过检测阈值的首次时间。在此，我们将治疗后反弹重新表述为随机首次通过问题，成功重新激活事件以时间依赖性强度到达，每个事件引发指数增长的病毒谱系。总血浆病毒载量因此是泊松散粒噪声过程，反弹对应于其首次阈值穿越。在罕见重新激活 regime中，这种穿越由最早成功的谱系主导。反弹时间 then分为两个组成部分：潜伏库重新激活的随机等待时间和检测到的确定性增长延迟。这种分离给出了移位危险生存定律，并给出了恒定激活、ART洗脱依赖性激活、免疫周期性激活、考克斯过程激活和异质库激活的封闭形式反弹时间分布。相同的公式还提供了适用于ATI试验的区间删失抽样结构的似然性。
英文摘要
In our earlier work, we modeled the stochastic initiation of HIV rebound by treating latent-cell reactivation as a Poisson-driven process during antiretroviral-therapy (ART) washout, immune modulation, and therapeutic perturbation~\cite{Taye2025CM}. That framework characterized activation survival, cumulative hazards, waiting-time laws, and expected viral-load trajectories. However, the endpoint observed in analytical treatment interruption (ATI) studies is not the hidden time of first successful reactivation. It is the first time at which plasma virus exceeds an assay-defined detection threshold. Here we reformulate post-treatment rebound as a stochastic first-passage problem, with $T_{\rm reb}=\inf\{t\ge t_w:V(t)\ge V_{\rm det}\}$. Successful reactivation events arrive with a time-dependent intensity, and each event seeds an exponentially expanding viral lineage. The total plasma viral load is therefore a Poisson shot-noise process, and rebound corresponds to its first threshold crossing. In the rare-reactivation regime, this crossing is dominated by the earliest successful lineage. Rebound timing then separates into two components: a stochastic waiting time for reservoir reactivation and a deterministic growth delay to detectability. This separation gives a shifted-hazard survival law and yields closed-form rebound-time distributions for constant activation, ART-washout-dependent activation, immune-periodic activation, Cox-process activation, and heterogeneous-reservoir activation. The same formulation also provides a likelihood suitable for the interval-censored sampling structure of ATI trials.
Comments35 pages
