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arxiv: 2604.20069 · v1 · submitted 2026-04-22 · 📊 stat.AP

Recognition: unknown

Bayesian inference for disease transmission models informed by viral dynamics

Andrew J. Black, Dylan J. Morris, Lauren Kennedy

Pith reviewed 2026-05-09 23:43 UTC · model grok-4.3

classification 📊 stat.AP
keywords Bayesian inferencemultiscale modelsviral dynamicshousehold transmissiondisease outbreaksparameter estimationcut modelsstochastic transmission
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The pith

A multiscale Bayesian model links viral load trajectories to household transmission parameters via a cut inference approach.

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

The paper builds a model that connects detailed individual viral load changes inside people to the random spread of infection between people in the same household. It introduces a cut method for Bayesian fitting that lets viral data shape estimates of when infections occur and when symptoms start, while avoiding the full computational cost of simultaneous inference across scales. The approach is tested on simulated outbreak data to check how well parameters can be recovered and how sampling frequency affects the results. Recovery stays unbiased as long as viral loads are sampled often enough. When samples are taken less frequently, some bias appears but can be reduced by bringing in additional viral load information from outside the main dataset.

Core claim

We propose a multiscale model that jointly captures heterogeneous individual-level viral load trajectories and stochastic household transmission, and develop efficient inference methods to fit it to data. Since full joint inference is computationally difficult, we employ a cut approach that passes information from the within-host to the between-host model but not vice versa. This enables the data on viral loads to inform the transmission parameters such as the infection times and symptom onset thresholds. We evaluate the framework on simulated household outbreak data, assessing parameter recovery, computational efficiency, and the effect of viral load sampling frequency on inference quality.

What carries the argument

The unidirectional cut inference method that feeds within-host viral load information into the between-host transmission model without feedback.

If this is right

  • Viral load observations can directly sharpen estimates of infection timing and symptom thresholds in household outbreaks.
  • The cut method keeps computation feasible while still letting individual-scale data inform population-scale transmission parameters.
  • Sparse viral sampling introduces bias that external viral load datasets can partially correct.
  • The framework supports joint analysis of heterogeneous viral trajectories and stochastic transmission events.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This structure could support real-time analysis of outbreak data by updating transmission estimates as new viral measurements arrive.
  • The same cut technique might transfer to other multiscale disease models where full joint fitting remains intractable.
  • Accounting for measurement error in viral loads within the within-host component could further reduce bias under sparse sampling.

Load-bearing premise

The one-way cut from viral dynamics to transmission parameters is enough to keep estimates of infection times and symptom thresholds accurate and unbiased.

What would settle it

A simulation with high-frequency viral load sampling that still produces biased estimates of household infection times would disprove the unbiased recovery result.

Figures

Figures reproduced from arXiv: 2604.20069 by Andrew J. Black, Dylan J. Morris, Lauren Kennedy.

Figure 1
Figure 1. Figure 1: (A) A realisation of the within-host viral load trajectory (blue), with the corresponding force of infection (orange) [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: An example outbreak in a household of size 4 over [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Plate diagram illustrating the two-stage within-host and between-host inference approach. Solid arrows denote [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Posterior summaries for the within-host parameters, shown as 95% credible intervals and grouped by number of [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Posterior summaries for the between-host parameters for each data replicate, shown as 95% credible intervals and [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Predictive distributions for d ⋆ by number of households (shown as panel titles). The prior predictive is indicated by the dashed black line, while blue lines correspond to posterior predictive distributions for different dataset sizes. The observed data used in the respective models is shown as a grey histogram. key dynamics necessary for accurate inference. To view the effect of these differences in infe… view at source ↗
Figure 7
Figure 7. Figure 7: Predictive distributions for d ⋆ (for H = 100 households) shown as violin plots for each dataset. Black dots indicate the observed d ⋆ and are jittered horizontally and partially transparent to reduce overplotting and provide a visual approximation to the distribution. 2 4 µω 0.00 0.25 0.50 0.75 1.00 Density (A) 0.05 0.10 0.15 η 0 10 20 30 Density (B) 0.0 2.5 5.0 d ? 0.0 0.2 0.4 Density (C) Daily 3-Days 5-… view at source ↗
Figure 8
Figure 8. Figure 8: (A, B) Marginal posterior distributions for the transmission parameters, [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Inference results for an outbreak in a household of four individuals under the various sampling regimes. Posterior [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Posterior predictive viral load trajectories for a single individual in the example dataset under the different [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: (A, B) Marginal posterior distributions for the transmission parameters under the different within-host data [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
read the original abstract

Infectious disease dynamics operate across multiple biological scales, with within-host viral dynamics being a key driver of between-host transmission. However, while models that explicitly link these scales exist, none have been developed with statistical inference as a primary goal. In this paper we propose a multiscale model that jointly captures heterogeneous individual-level viral load trajectories and stochastic household transmission, and develop efficient inference methods to fit it to data. Since full joint inference is computationally difficult, we employ a cut approach that passes information from the within-host to the between-host model but not vice versa. This enables the data on viral loads to inform the transmission parameters such as the infection times and symptom onset thresholds. We evaluate the framework on simulated household outbreak data, assessing parameter recovery, computational efficiency, and the effect of viral load sampling frequency on inference quality. Parameter recovery is unbiased when the sampling frequency of the viral loads is high enough. When sampling is sparse, some bias is introduced, but incorporating external viral load data can mitigate this.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a multiscale Bayesian model integrating heterogeneous individual-level viral load trajectories with stochastic household transmission, using a one-way cut inference procedure to pass information from the within-host model to the between-host model without feedback. This enables estimation of transmission parameters such as infection times and symptom onset thresholds. The approach is evaluated solely on simulated household outbreak data, with claims of unbiased parameter recovery at high viral-load sampling frequencies and bias mitigation via external data when sampling is sparse.

Significance. If the cut approximation is shown to be robust beyond the simulated setting, the work offers a practical route to linking within-host and between-host scales for infectious disease modeling, with direct implications for improving estimates of key epidemiological quantities like infection timing.

major comments (2)
  1. [Inference Methods] The central claim of unbiased recovery of infection times and symptom-onset thresholds rests on the cut procedure (described in the inference section) that feeds point summaries or marginal posteriors from the within-host model into the household transmission model without feedback. The manuscript supplies no analytic bound on the resulting approximation error nor a small-scale comparison to full joint inference, which is load-bearing for the unbiasedness result when the two scales may be more tightly coupled than assumed.
  2. [Simulation Study] All parameter-recovery results (including the high-sampling-frequency unbiasedness statement) are obtained from data generated from the identical model used for fitting. This design cannot reveal distortion under realistic misspecification or when within-host and between-host dynamics are not cleanly separable, undermining the general claim that the cut produces accurate transmission-parameter estimates.
minor comments (2)
  1. [Abstract] The abstract states that 'parameter recovery is unbiased when the sampling frequency of the viral loads is high enough' but provides no quantitative threshold for 'high enough' nor any error-bar or coverage details from the simulations.
  2. [Results] Computational-efficiency claims are mentioned but lack concrete metrics (e.g., wall-clock time, effective sample size) or comparisons to alternative samplers.

Simulated Author's Rebuttal

2 responses · 2 unresolved

We thank the referee for their constructive comments. We address each major point below, acknowledging the limitations of the cut approximation and the simulation design while clarifying the scope of our claims. We will make targeted revisions to improve transparency without altering the core methodology or results.

read point-by-point responses

  1. Referee: [Inference Methods] The central claim of unbiased recovery of infection times and symptom-onset thresholds rests on the cut procedure (described in the inference section) that feeds point summaries or marginal posteriors from the within-host model into the household transmission model without feedback. The manuscript supplies no analytic bound on the resulting approximation error nor a small-scale comparison to full joint inference, which is load-bearing for the unbiasedness result when the two scales may be more tightly coupled than assumed.

    Authors: We agree that the cut procedure is an approximation whose error lacks an analytic bound in the manuscript, and that a direct comparison to full joint inference would be valuable for assessing performance when scales are tightly coupled. Full joint inference is computationally prohibitive for the full model, which motivated the cut approach as described in the inference section. Our simulations demonstrate unbiased recovery of transmission parameters under frequent sampling when the model is correctly specified. We will revise the manuscript to include an expanded discussion of the cut approximation, its assumptions, and potential limitations, and we will add a small-scale numerical comparison on a reduced model where joint inference is feasible. revision: partial

  2. Referee: [Simulation Study] All parameter-recovery results (including the high-sampling-frequency unbiasedness statement) are obtained from data generated from the identical model used for fitting. This design cannot reveal distortion under realistic misspecification or when within-host and between-host dynamics are not cleanly separable, undermining the general claim that the cut produces accurate transmission-parameter estimates.

    Authors: We acknowledge that the simulation study generates data from the same model used for fitting, which is standard practice for validating inference procedures but does not address misspecification or non-separable dynamics. The manuscript claims unbiased recovery specifically when viral-load sampling is frequent and the model assumptions hold; it does not assert general robustness to misspecification. We will revise the text to explicitly qualify the unbiasedness result as holding under correct model specification, add a limitations paragraph discussing potential biases under misspecification, and note that robustness checks are left for future work. revision: partial

standing simulated objections not resolved
  • Deriving a general analytic bound on the approximation error induced by the cut procedure for this multiscale model.
  • Conducting a full-scale comparison between cut and joint inference due to prohibitive computational cost.

Circularity Check

0 steps flagged

No significant circularity detected in the multiscale inference derivation.

full rationale

The paper defines a joint multiscale generative model for viral loads and household transmission, then applies a standard one-directional cut approximation to enable tractable inference by passing within-host summaries to the transmission model without feedback. Parameter recovery is validated on data simulated from the same model, which is a conventional external check rather than a self-referential fit. No equations reduce a claimed prediction to a fitted input by construction, no uniqueness theorems are imported from self-citations, and no ansatz or renaming of known results is presented as a derivation. The central claims rest on the explicit modeling choices and simulation benchmarks, which remain independent of the target posterior.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model rests on standard stochastic assumptions for viral trajectories and household transmission plus the validity of the cut inference separation; multiple transmission and viral parameters are fitted to simulated data.

free parameters (2)
  • infection times and symptom onset thresholds
    Estimated from viral load data via the cut procedure and used to inform transmission parameters.
  • transmission rate parameters
    Fitted within the between-host stochastic model informed by within-host outputs.
axioms (2)
  • domain assumption Viral load trajectories can be modeled as heterogeneous individual-level processes that drive transmission probability.
    Invoked to link the two scales in the multiscale model.
  • ad hoc to paper One-way cut inference preserves unbiased estimation of transmission quantities.
    Central to the computational strategy described in the abstract.

pith-pipeline@v0.9.0 · 5468 in / 1455 out tokens · 24146 ms · 2026-05-09T23:43:34.397450+00:00 · methodology

discussion (0)

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Reference graph

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