发表机构
Universidad de Guanajuato; Université Catholique de Louvain（瓜纳华托大学; 天主教鲁汶大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用随机场理论和瞬子动力学，将HIV潜伏期建模为随机过程，推导出病毒反弹的平均首通时间，预测典型患者约6个月反弹，与临床观察一致。
AI 中文摘要
从临床潜伏期到活动性HIV感染的转变是一个随机过程。基于常微分方程（ODEs）的传统确定性模型无法捕捉灭绝边界及随后的病毒反弹，因为这些模型忽略了小种群极限下的人口统计学噪声。我们利用Doi-Peliti二次量子化形式，将由此产生的Master方程映射到相干态路径积分上，并验证了随机哈密顿量在经典流形$\bar{\phi}_i = 1$上能正确重现平均场ODEs。在半经典（大系统尺寸）极限下，我们推导出八个耦合的Hamilton-Jacobi方程，识别出无病毒和流行病的固定点，并获得了四物种网络的基本再生数$R_0$。对于解析可处理的单病毒粒子爆发（$n=1$）情况，我们证明随机哈密顿量可分解为两个双线性项，揭示了一个构成瞬子轨迹的非平凡零能量面。随后，准稳态约化产生一阶线性ODE，其闭式解以生物学参数给出了瞬子作用量$S_{\rm inst}$。通过校准临床数据——感染细胞半衰期$\delta_I^{-1}\approx 2\\,\rm d$、病毒爆发大小$N\approx 10^3$、清除率$\delta_V\approx 23\\,\rm d^{-1}$、再激活率$\eta\approx 10^{-3}\\,\rm d^{-1}$以及潜伏库大小$L_0\approx 10^6$个细胞——我们得到典型患者病毒反弹的平均首通时间（MFPT）约为6个月，根据库大小不同，范围从几天到几年不等。这些预测与观察到的治疗中断后反弹时间尺度定性一致。
英文摘要
The transition from clinical latency to active HIV infection is a stochastic process. Traditional deterministic models based on ordinary differential equations (ODEs) fail to capture the extinction boundary and the subsequent rebound of the virus because they neglect demographic noise in the small-population limit. We map the resulting Master Equation onto a coherent-state path integral using the Doi-Peliti second-quantization formalism and verify that the stochastic Hamiltonian reproduces the correct mean-field ODEs on the classical manifold $\barϕ_i = 1$. In the semiclassical (large system-size) limit we derive eight coupled Hamilton-Jacobi equations, identify the virus-free and endemic fixed points, and obtain the basic reproduction number $R_0$ for the four-species network. For the analytically tractable case of single-virion bursting ($n=1$) we show that the stochastic Hamiltonian \emph{factorizes} into two bilinear terms, exposing a non-trivial zero-energy surface that constitutes the instanton trajectory. A quasi-steady-state reduction then yields a first-order linear ODE whose closed-form solution gives the instanton action $S_{\rm inst}$ in terms of biological parameters. Calibrating to clinical data---infected-cell half-life $δ_I^{-1}\approx 2\,\rm d$, viral burst size $N\approx 10^3$, clearance rate $δ_V\approx 23\,\rm d^{-1}$, reactivation rate $η\approx 10^{-3}\,\rm d^{-1}$, and latent reservoir size $L_0\approx 10^6$ cells---we obtain a mean first-passage time (MFPT) to viral rebound of $\approx 6$ months for a typical patient, with a range of days to years depending on reservoir size. These predictions are qualitatively consistent with observed post-interruption rebound timescales.
Comments12 pages, 2 figures
