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Stochastic First-Passage Theory of HIV Viral Rebound Following Latent Reservoir Reactivation

T0 review · 2 major / 6 minor · reviewed 2026-07-14 · grok-4.5

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Pith's one-line read HIV rebound after treatment stop is a first threshold crossing, not the moment a latent cell reactivates, and that delay grows only with the log of the assay threshold.

desk verdict Clean first-passage reformulation of the ATI endpoint with usable closed forms and a quantified single-founder error; solid enough to send to referees. read the letter →

arxiv 2607.04910 v2 pith:VFB5KKQO submitted 2026-07-06 physics.bio-ph

Mesfin Asfaw Taye This is my paper · ORCID
classification physics.bio-ph
keywords HIVreboundlatentreservoirfirst-passagetimestochasticreactivationPoissonprocessviralloadARTinterruptiondetectionthreshold
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Clinical rebound after antiretroviral interruption is the first time an individual's plasma viral load crosses a detection threshold, not the hidden moment a latent cell reactivates and not the time when the average viral load would cross that line. Successful reactivations arrive as a Poisson process and each seeds an exponentially growing lineage, so the total viral load is shot noise. When reactivations are rare, the first established lineage dominates, so rebound time splits into a random waiting time plus a fixed growth delay that depends logarithmically on the assay threshold. That split produces simple shifted-hazard survival laws for constant, washout, periodic, fluctuating, and multi-class reservoirs, and it yields a likelihood that matches the interval-censored sampling used in analytical treatment interruption trials. Threshold-resolved median rebound times of roughly 16, 21 and 32 days at 50, 400 and 10,000 copies per millilitre fit an effective net growth rate near 0.33 per day, lower than maximal early-infection growth.

What carries the argument

The single-founder first-passage decomposition of the Poisson shot-noise viral load: rebound is identified with the first successful reactivation time delayed by the deterministic growth-to-detection lag τ_det, converting any successful-reactivation intensity λ(t) into a shifted cumulative-hazard survival law.

What would settle it

In an ATI cohort with frequent viral-load sampling, test whether the median time to rebound rises linearly with log of the detection threshold at slope near 1/0.33 day; a clear departure from that slope, or systematic multi-lineage cooperative crossings that advance rebound beyond the single-founder prediction, would refute the central separation.

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Extended reading notes

Core claim

In the rare-reactivation regime the first successful expanding lineage dominates the threshold crossing, so the observed rebound time separates as T_reb ≈ T_1 + τ_det with τ_det = τ_e + r^{-1} log(V_det / v_0). The resulting shifted-hazard survival P(T_reb > t) ≈ exp(-∫_{t_w}^{t-τ_det} λ(s) ds) supplies closed-form rebound-time laws for constant, washout-dependent, immune-periodic, Cox-process and heterogeneous-reservoir activation, and it supplies an interval-censored likelihood for ATI data that predicts logarithmic dependence of median rebound on detection threshold.

Load-bearing premise

That the earliest successful lineage alone drives the crossing, so the chance that several still-undetectable lineages add up and cross the threshold first can be neglected.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. The manuscript reformulates post-ART HIV rebound as a first-passage problem for a Poisson shot-noise viral load, T_reb = inf{t ≥ t_w : V(t) ≥ V_det}, rather than as the hidden first reactivation time. In the rare-reactivation regime it invokes a single-founder approximation T_reb ≈ T_1 + τ_det with τ_det = τ_e + r^{-1} log(V_det/v_0), yielding the shifted-hazard survival P(T_reb > t) ≈ exp(-∫_{t_w}^{t-τ_det} λ(s) ds) and closed-form rebound laws for constant, ART-washout, periodic, Cox-process, and heterogeneous-reservoir intensities. It supplies an interval-censored ATI likelihood and predicts logarithmic dependence of median rebound on V_det; a three-median consistency check against Gunst et al. gives an effective growth rate r ≈ 0.33 day^{-1}.

Significance. If the first-passage separation and shifted-hazard laws hold, the paper cleanly bridges activation-survival models to the endpoint ATI trials actually measure, and it does so with standard, correctly executed Poisson and Laplace-transform machinery (Props. 1–2, Appendices A–F). Strengths include explicit quantification of single-founder error against full cooperative Monte Carlo (Table 2, Fig. 3), closed forms across several biologically motivated intensities, a likelihood that respects interval censoring, and a falsifiable logarithmic-threshold prediction. These are useful analytical tools for ATI design and for interpreting why maximal early-infection growth rates underpredict observed rebound times.

major comments (2)
  1. §4.2 and Table 2 quantify single-founder median error at r = 0.69 day^{-1} (τ_d ≈ 5.7 d), where baseline λτ_d ≈ 1.7 already yields ~5% overestimation and λτ_d ≈ 3 yields ~10%. The ATI-calibrated regime of §6 uses r ≈ 0.33 day^{-1}, which roughly doubles τ_d (≈ 11–12 d at V_det = 50) and therefore λτ_det at the same λ. The paper does not recompute the cooperative error or survival bias under those calibrated parameters, yet the abstract and §6 present the shifted-hazard laws as the working description of ATI rebound. Please either (i) re-run the Table 2 comparison at r ≈ 0.33 (and at the 400 and 10,000 thresholds) or (ii) restrict the quantitative claims and the likelihood in §6 to the regime where λτ_det is shown to keep the bias small, and state the cooperative correction of Appendix F as the default when that condition fails.
  2. §6 and Fig. 6 fit Q_{0.5} = C + r^{-1} log V_det to three cohort-level medians (50, 400, 10,000 copies/mL), obtaining r ≈ 0.33 day^{-1} and R^{2} ≈ 0.99. With two free parameters and three points this is a consistency check, as the text notes, but the abstract states that the medians “support this dependence” and “imply” r ≈ 0.33. That language overstates what three aggregated medians can identify: C absorbs the free combination t_w + τ_e + (log 2)/λ - r^{-1} log v_0, and no individual-level or interval-censored fit is shown. Please temper the abstract and §6 wording to “consistent with” rather than “imply,” report sensitivity of r to plausible v_0 and assay-unit choices, and, if space allows, illustrate the §6 likelihood on a small published ATI interval-censored sample so that the inference claim is demonstrated rather than only derived.
minor comments (6)
  1. Eq. (1) and Eq. (22) omit the eclipse phase in one place and include it in another; a single consistent expression for E[T_reb] early in the introduction would help.
  2. Figure 2 caption and main text use V_det = 50 with r = 0.69; consider adding a panel or note at the calibrated r ≈ 0.33 so the visual matches the ATI discussion in §6.
  3. Notation: λ(t) is redefined as successful (establishment-weighted) intensity relative to the earlier activation-survival paper; a short explicit mapping λ = p_est λ_act in the introduction (beyond §3) would reduce confusion for readers of both papers.
  4. Table 1 lists λ baseline 0.30 day^{-1} while the ATI discussion prefers λ_eff ≈ 0.17–0.20; flag which column is used in each figure to avoid mixing regimes.
  5. Appendix D quantile formula with the Lambert W function is useful; a one-line numerical check against the series mean (Eq. 71) would reassure readers implementing the washout law.
  6. References [28]–[117] include many items only loosely related to HIV rebound; trimming to works that are actually cited in the argument would improve focus.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: shifted-hazard first-passage laws follow from Poisson + exponential-growth axioms; Gunst calibration is an explicit consistency check, not a forced prediction; self-citation of prior activation paper is contextual only.

full rationale

The core derivation (T_reb ≈ T_1 + τ_det with τ_det = τ_e + r^{-1} log(V_det/v_0), yielding the shifted cumulative-hazard survival of Prop. 2 / Eq. (44) and the closed forms of §§5.1–5.5) is obtained directly from the model axioms of inhomogeneous Poisson successful-reactivation events and monotone exponential lineage growth; the single-founder approximation is stated as an upper bound whose error is quantified by simulation (Table 2) rather than hidden. The logarithmic threshold dependence is likewise a model consequence (Eq. (95)); the three Gunst medians are used only to extract an effective r ≈ 0.33 day^{-1} and are labeled a “consistency check rather than full parameter validation,” so the fit is not re-presented as an independent prediction. The sole self-citation of the author’s 2025 activation-survival paper supplies the earlier Poisson intensity constructions that are re-derived and re-interpreted here; it is not load-bearing for the first-passage claim. No uniqueness theorem, ansatz smuggling, or definitional tautology appears. Score 1 reflects only the minor, non-load-bearing self-citation.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central claim rests on standard Poisson and exponential-growth axioms plus a small set of physiologically motivated free parameters taken from the literature or fitted to three external medians. No new physical entities are postulated; the single-founder approximation is an explicit modeling choice whose error is quantified.

free parameters (6)
  • successful reactivation rate λ (or λ0) = 0.30 day^{-1} (baseline); effective 0.17–0.20 for ATI calibration
    Baseline 0.30 d^{-1} (range 0.17–0.54) taken from HIV/SIV interruption studies; enters every waiting-time formula and is re-interpreted as pest·λ_act.
  • net growth rate r = 0.33 day^{-1} (ATI fit); 0.69 (baseline examples)
    Baseline 0.69 d^{-1} from classical viral dynamics; effective value 0.33 d^{-1} fitted by linear regression of three Gunst medians vs log V_det.
  • founder output v0 = 1 cp/mL
    Effective plasma-equivalent scale of one established lineage; set to 1 cp/mL; only logarithmic dependence.
  • eclipse delay τe = 1 day
    RNA-appearance lag; baseline 1 day (range 0.5–2); absorbed into τ_det.
  • washout parameters A0, k_drug = A0=1, k_drug=0.3 day^{-1}
    Initial residual suppression and drug elimination rate; A0=1, k_drug=0.3 d^{-1} used in examples.
  • Cox fluctuation intensity D (or σ) = 0.10 day^{-1} (example)
    Variance of integrated random hazard; example D=0.10 d^{-1} used to illustrate overdispersion.
assumptions (4)
  • domain assumption Successful established reactivations form an inhomogeneous Poisson process with intensity λ(t) = pest(t) λ_act(t).
    Standard for rare independent reactivation events; stated in §3 and Appendix A.
  • domain assumption Each established lineage contributes v0 exp(r(t-Ti)) with constant net growth r>0, rendering V(t) monotone.
    Enables the exact first-passage identity {T_reb ≤ t} = {V(t) ≥ V_det}; §3–4.
  • ad hoc to paper In the rare-reactivation regime the earliest founder dominates, so cooperative multi-lineage crossing may be neglected (single-founder approximation).
    Core modeling reduction of Proposition 2; error quantified but not eliminated.
  • standard math Laplace functional of a Poisson random measure yields the closed-form transform of the shot-noise viral load.
    Kingman/Feller identity used in Proposition 1 and Appendix B.

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Cite this review

Pith. "Pith review of Stochastic First-Passage Theory of HIV Viral Rebound Following Latent Reservoir Reactivation." pith.science (2026). https://pith.science/paper/VFB5KKQO

@misc{pith2026260704910,
  author       = {Pith},
  title        = {Pith review of: Stochastic First-Passage Theory of HIV Viral Rebound Following Latent Reservoir Reactivation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VFB5KKQO}},
  note         = {Machine review of arXiv:2607.04910}
}
abstract

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.

Figures

Figures reproduced from arXiv: 2607.04910 by the authors.

Figure 1
Figure 1. First-passage formulation of HIV viral rebound after ART interruption. Before interruption, [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Representative shot-noise viral-load trajectories [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Mean-field threshold crossing versus stochastic first passage in a rare-reactivation regime. [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Effect of pharmacokinetic ART washout on rebound survival, from the shifted cumulative [PITH_FULL_IMAGE:figures/full_fig_p019_4.png]
Figure 5
Figure 5. Figure 5: Competing reservoir classes as shifted first-arrival processes, from the constant-rate [PITH_FULL_IMAGE:figures/full_fig_p022_5.png]
Figure 6
Figure 6. Figure 6: Threshold-dependence consistency check using the Gunst et al. ATI meta-analysis [ [PITH_FULL_IMAGE:figures/full_fig_p024_6.png]

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Pith tools

Reviewed July 14, 2026 · model on record in the stance chip above.