Accounting for contact network uncertainty in epidemic inferences

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Public source manuscript

These findings are tied to a public preprint: arXiv:2404.02924 · q-bio.PE / Statistics — applications

Open source

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What a reviewer will push on first

The most severe issues a reviewer will raise, named. Each jumps to the full critique below.

The catch a generic AI would miss

Statistical auditSec. 4.2

Negative-binomial probability parameter has both a fixed value and a Gamma prior — at least one must be wrong

Section 4.2 defines the network observation likelihood as $X_{w}^{ij} ∣ A_{w}^{ij} = 0 \sim NegBin (n_{0 w}, p_{0 w})$ and $X_{w}^{ij} ∣ A_{w}^{ij} = 1 \sim NegBin (n_{1 w}, p_{1 w})$ . It then says "we will fix $p_{0 w} = 1$ for all w" but the priors block declares $p_{0 w} \sim Gamma (2, 4)$ . $p_{0 w}$ is therefore both a fixed constant and a sampled parameter — a contradiction that any HMC implementation will silently resolve in favor of one or the other.

Editorial verdict

Do not submit yet — strong premise, model-definition gaps, missing reproducibility package

Likely outcome if submitted today: desk reject — chiefly because of missing journal-required elements (Author Summary for PLOS Comput. Biol., ethics/permit statement for the dolphin field data, public availability for analysis data and code, complete references), but also because the dolphin disease model is internally contradictory (described as SIR but using an exposed state E with no E→I transition specified) and the network observation model has a parameter that is simultaneously fixed and assigned a Gamma prior on a [0,1]-bounded probability.

Read the full editorial recommendation

The statistical premise — joint posterior over epidemic parameters and a latent contact network using MDN-ABC — is genuinely strong and the simulation calibration is the right scaffolding. The single most important fix this week is to rewrite the methods around a single explicit generative model for each study (one for the simulation, one for the dolphin application), with a compact table defining every latent variable, observed variable, parameter, prior, time scale, transition rule, and sampling step. Once that table exists, most of the contradictions below collapse into one or two lines of clarifying text.

Recommended target: PLOS Computational Biology remains plausible after substantial revision, especially if framed as a simulation-based inference method for epidemics on uncertain networks. Cascade fallback: Epidemics or Journal of Theoretical Biology if method validation is strengthened; PLOS ONE only if the paper remains primarily a demonstration. Time to submission readiness: 6–10 weeks of focused revision, assuming code/data deposition and additional validation can be completed promptly.

Quality scorecard

Overall · 3.0/5

Originality

3/5

The combination of MDN-ABC with the Young et al. network sampling framework is a genuine methodological integration, but each component is previously published and the novelty is primarily in their assembly rather than any new theoretical contribution.

Importance of research question

4/5

Accounting jointly for contact network uncertainty and partially observed epidemic histories is a real and underserved problem in network epidemiology, with direct relevance to field studies like the dolphin dataset.

Claims are well-supported

3/5

The simulation study demonstrates posterior concentration and reasonable calibration, but the coverage plots (Fig. 4) show systematic undercoverage at low nominal levels that the authors do not adequately address, and the dolphin application lacks a formal goodness-of-fit comparison against a simpler baseline.

Experimental soundness

3/5

The coverage test with 5000 instances is appropriate, but the simulation study uses a single "true" epidemic realization as ground truth, the network size is never stated, and the Weibull infectious period model for the dolphin application is not validated against alternatives.

Clarity of writing

2/5

Multiple figures have illegible or missing axis labels (Fig. 2 panels are described only by letter with no axis annotation visible in the text, Fig. 4 axes are cryptically labeled), and the notation section introduces symbols that are later used inconsistently (At vs. A throughout).

Value to community

3/5

The framework is genuinely flexible and the dolphin case study is a compelling demonstration, but without released code and a cleaner presentation, practical adoption will be limited.

Prior work contextualization

3/5

The authors engage with the core ABC and network inference literature, but do not discuss the broader network epidemiology review literature (e.g., Danon et al., 2011) and do not compare against the most relevant competing method, Almutiry and Deardon (2020), beyond a brief mention.

Detailed findings

High severity.
#1MethodologySec. 4.1; Discussion
The dolphin disease model is described as SIR but uses an exposed state E with no E→I transition specified
In the compartmental SIR model, nodes can take on one of three states
Section 4.1 says: "we will model TSD as a discrete-time SIR process," but then defines node state $W_{t}^{i} \in {S, E, I, R}$ and writes transmission probabilities into $E$ (e.g. $β_{c} = P (W_{t + Δ t}^{i} = E via j ∣ \dots)$ ). No transition rule from $E \to I$ is given anywhere. The Discussion then states "we modeled TSD as a simple SIR disease, which assumes that the incubation period for TSD is short relative to our simulation time-steps" — but a "short incubation" is not a substitute for actually defining whether the model is SIR or SEIR.
This is the load-bearing model for the entire empirical application. A reviewer reading Section 4.1 cannot tell whether the dolphin posteriors are conditioned on an SIR likelihood (no latent compartment) or an SEIR likelihood (with a latent compartment of unspecified duration). The age-class susceptibility result — the headline empirical claim — depends on which one. Pick one model, write the transition rules cleanly, and remove the unused state from the other.
Suggested fix
Decide whether the TSD model is SIR or SEIR. If SIR, replace E with I throughout the infection transition and remove "exposed" language. If SEIR, add latent-period parameters (rate or distribution), state the E→I transition rule explicitly, and report a sensitivity analysis to the latent-period prior. The Discussion claim about "short incubation" then becomes an explicit modeling assumption rather than a hedge.
High severity.
#2MethodologySec. 4.1; Sec. 5; Discussion
Age-class susceptibility conclusion is partly pre-imposed by the priors, not learned from data
The headline empirical finding for the dolphin application — that calves are materially more susceptible than adults — depends on the choice of unequal priors over calf-class and adult-class transmission probabilities. The Discussion notes this in passing ("the age-class susceptibility result is partly driven by the choice of unequal priors") but the main text does not quantify how much of the posterior separability is data-driven versus prior-driven.
For PLOS Comput. Biol., this is the kind of conclusion a reviewer will isolate. The standard fix is to (a) report the posterior under matched priors over calf and adult susceptibility, (b) show the prior-to-posterior shift on a single panel for both classes, and (c) make a clean statement: "with matched priors, the calf-vs-adult posterior separation is X; with the differential priors used here, it is Y; the data contribute Z to the gap." That is the analysis a careful reader needs to assess the claim.
Suggested fix
Add a sensitivity-analysis subsection to Sec. 5 reporting the posterior under matched calf/adult susceptibility priors. Report the prior-to-posterior shift visually and quantify the data-driven vs. prior-driven contribution to the age-class result. If the result attenuates substantially under matched priors, soften the abstract claim.
High severity.
#3MethodologySec. 3
Simulation log-normal scenario uses an Erdős–Rényi observation model — interpret as misspecification, not as a network prior
Section 3 says the true network is either Erdős–Rényi with mean degree 4 or log-normal-degree with mean degree 4. The observation/sampling model assumes $A_{ij} \sim Bernoulli (ρ)$ , which is an Erdős–Rényi prior. Two interpretations are possible: (a) the log-normal scenario is a misspecified-prior experiment and the manuscript should say so explicitly; (b) the network prior should match the data-generating process for the log-normal case. The current text does neither.
This matters because the simulation studies are the manuscript's evidence that posterior coverage is well-calibrated. If the log-normal case is a misspecification experiment, the calibration claim becomes "calibrated under correctly specified network prior, gracefully degraded under misspecification" — which is a different and more interesting result than "calibrated under both" but also has different implications for the dolphin application (where the true contact distribution is unknown).
Suggested fix
Reframe Sec. 3 explicitly: "We use an Erdős–Rényi network prior throughout. The log-normal scenario tests robustness to network-prior misspecification; we do not claim calibration when the prior is wrong." Then either add a matching log-normal-prior comparison run, or note that doing so is straightforward but out of scope and that the dolphin application uses the more flexible prior described in Sec. 4.2.
High severity.
#4Statistical auditSec. 4.2
Negative-binomial probability parameter has both a fixed value and a Gamma prior — at least one must be wrong
Section 4.2 defines the network observation likelihood as $X_{w}^{ij} ∣ A_{w}^{ij} = 0 \sim NegBin (n_{0 w}, p_{0 w})$ and $X_{w}^{ij} ∣ A_{w}^{ij} = 1 \sim NegBin (n_{1 w}, p_{1 w})$ . It then says "we will fix $p_{0 w} = 1$ for all w" but the priors block declares $p_{0 w} \sim Gamma (2, 4)$ . $p_{0 w}$ is therefore both a fixed constant and a sampled parameter — a contradiction that any HMC implementation will silently resolve in favor of one or the other.
Two further problems compound this. First, $p_{1 w}$ has no prior at all. Second, a Gamma prior is generally invalid for a probability parameter constrained to $[0, 1]$ — Gamma puts mass on values larger than 1. The standard parametric choice for a probability parameter is a Beta. If the negative-binomial is parameterized in mean-dispersion form instead ( $μ, θ$ ), positive priors on those parameters are fine but $p_{0 w}$ should not appear in the prior block.
Suggested fix
Choose one parameterization. If keeping the (n, p) form: declare p₀w as fixed in the model spec, remove it from the prior block, add a Beta(α, β) prior on p₁w, and verify your HMC sampler is treating each parameter consistently. If switching to mean-dispersion: rewrite Eq. (4.2) in terms of (μ, θ), specify positive priors on both, and remove all p references. Add a one-line "we use the (n, p) parameterization with p as a probability parameter" or equivalent note.
Medium severity.
#5Novelty assessmentSec. 1; Sec. 7
Positioning vs Sherborne et al., Stack et al., and the SBI literature is left implicit
In this paper, we will focus on the use of the Mixture Density Network-compressed ABC (MDN-ABC)
The Introduction motivates contact-network uncertainty as an open problem but does not separate this work's contribution from three near neighbors: (a) Sherborne et al. 2018 (PLOS Comput. Biol.), which fits epidemic models on partially observed networks; (b) Stack et al. 2021 (Theor. Popul. Biol.), which infers networks from epidemic data; and (c) the broader simulation-based-inference literature (Greenberg-Nonnenmacher-Macke ICML 2019, Papamakarios-Murray NeurIPS 2016) which has produced several MDN-style approaches in the last 5 years.
A reviewer at PLOS Comput. Biol. who knows any of these three lines will look for a one-paragraph statement of what this paper adds: e.g. "(a) is method development without a real-world application; (b) infers networks from epidemic data alone, not jointly; (c) is general SBI machinery not specialized to epidemic-network joint inference. The present work specializes the MDN-ABC framework to the joint epidemic-network setting and demonstrates calibration on simulated data plus a real Shark Bay dolphin application." That paragraph does not exist in the current draft.
Suggested fix
Add a "Related work" paragraph at the end of Sec. 1 (or a short Sec. 1.1) explicitly distinguishing this work from Sherborne, Stack, Greenberg-Nonnenmacher-Macke, and Papamakarios-Murray. Three sentences each, with the contrast spelled out. This converts an asserted contribution ("we develop") into a positioned contribution ("we develop X, which extends Y by Z").
High severity.
#6Internal consistencySec. 3
Binary disease-status labels are reversed in the simulation description
Section 3 states: "We periodically observe the binary disease status of each node: 'infected' for nodes in the susceptible or recovered state, and 'not infected' for nodes in the infected state." This contradicts the next sentence: "The status of the node is considered to be 1 if the node is infected, and 0 if the node is susceptible or recovered." A reviewer reading either definition will lose confidence in the simulation pipeline until the contradiction is resolved.
Suggested fix
Change the first sentence to say "not infected" for susceptible/recovered and "infected" for infected. Both statements should match the natural convention.
Medium severity.
#7Internal consistencySec. 3
Continuous-time SIR rate definitions conflict with discrete-time simulation language
Section 3 defines transmission and recovery as continuous-time-Markov rates, $β = lim_{Δ t \to 0} (\dots) /Δ t$ and similarly for $γ$ . But the same section says "We continue our simulated epidemic for 50 timesteps" and observes every 7 timesteps, language that fits a discrete-time approximation rather than a continuous-time Markov simulator. The reader cannot tell which one was implemented.
Suggested fix
State explicitly: "We simulate the continuous-time Markov SIR process via the Doob–Gillespie algorithm and record observations at discrete times t ∈ {0, 7, 14, ...}." If a discrete-time approximation was actually used, define the per-step transition probabilities directly and remove the continuous-time-rate definitions.
Low severity.
#8Internal consistencySec. 4.1
Weibull infectious-period parameters use two different notations in the same paragraph
Section 4.1 defines: "The duration of infectiousness is distributed as a Weibull distribution with shape $γ_{a}$ and scale $γ_{b}$ ." The priors are then written as $γ_{k} \sim Uniform (0.2, 5)$ and $γ_{λ} \sim Uniform (10, 160)$ . The reader has to infer that $γ_{k} \equiv γ_{a}$ (shape) and $γ_{λ} \equiv γ_{b}$ (scale).
Suggested fix
Use one notation throughout — γ_shape and γ_scale, or γ_a and γ_b — and update the prior block to match. Half a line of edit, but the kind of inconsistency that gets flagged in copy-edit anyway.
Low severity.
#10Internal consistencyMethods (Sec. 2.3); Appendix
A vs A_t / A_w: static-network and time-indexed-network notation are used inconsistently
The Methods define the true contact network as $A$ (static), but Section 2.3 and the Appendix use $A_{t}$ (time-indexed) — e.g. $P (A_{t}, ϕ ∣ X)$ and "we will treat $A_{t}$ as a nuisance parameter." This is mostly cosmetic but it does create one substantive ambiguity: in the dolphin application the network IS time-indexed by year ( $A_{w}$ ), and the reader cannot tell from notation alone whether the framework treats per-year networks as the same object as a static A.
Suggested fix
Use A for the static-network case (Sec. 3 simulation), A_w for the yearly dolphin networks, and never A_t — there is no per-timestep network object in this paper.
Low severity.
#12Figure critiqueFigs. 3, 5
Figure 3 legend lists 11 instance labels (0–10) but text says 10 instances; Figure 5 axis labels duplicated
Section 3 says "we re-simulate the original epidemic 10 times for each scenario" but Figure 3's legend appears to list 0 through 10 (11 labels). Figure 5 uses inconsistent time indexing — Section 4.2 defines yearly networks for w = 1, ..., 5, but the caption refers to "for time w = 0." Both will be flagged in copy-edit and are minor in isolation, but together they signal that the figure pass was rushed.
Suggested fix
Decide whether 10 or 11 instances are shown, relabel Fig. 3 accordingly. Pick one indexing convention for Fig. 5 and apply consistently.
High severity.
#13ReproducibilityMethods; end matter
No code repository, archived version, or software-version statement for an SBI methods paper
The manuscript names STAN as the implementation software ("Similar to [37], we will implement this model in STAN, which utilizes a Hamiltonian Monte Carlo algorithm") but does not provide a code repository, archived version, release tag, DOI, or software version. For a computational methods paper at PLOS Computational Biology, code availability is an explicit submission requirement; for a Mixture-Density-Network-compressor + ABC pipeline specifically, reviewers will not assess calibration claims without being able to re-run the analysis.
Suggested fix
Deposit the analysis code on GitHub with a Zenodo DOI for the version submitted. Add a Code Availability statement: "Analysis code, including the MDN training pipeline, ABC sampler, and simulation harness, is available at github.com/<repo> and archived at Zenodo doi:10.5281/zenodo.<id>. STAN version 2.35; Python version 3.11; full dependency list in environment.yml."
High severity.
#14Reporting guidelineEnd matter
PLOS Comput. Biol. requires an Author Summary; ethics/permit statement for animal field data is missing
PLOS Computational Biology requires every research article to include an Author Summary (a 150–200-word non-technical summary written for a broader audience). The manuscript does not include one. The Shark Bay dolphin work is observational field research on wild marine mammals; PLOS journals require an ethics statement covering field permits, animal-handling protocol approval, and the corresponding national/institutional regulatory authority (in Australia: typically a state-level Department of Biodiversity wildlife permit and university Animal Ethics Committee approval). Neither is present.
Suggested fix
Add an Author Summary section after the Abstract, 150–200 words, written for a non-specialist scientific audience. Add an Ethics Statement: "Field observations on wild Tursiops aduncus in Shark Bay, Western Australia, were conducted under [Permit / DBCA license number] and approved by the [University] Animal Ethics Committee under protocol [number]." If the permits/approvals are not yet obtained, this is a hard blocker for the submission.
Medium severity.
#15Submission readinessSubmission package
References are cited but the bibliography appears truncated; data availability statement is missing
The manuscript cites Sherborne, Stack, Beaumont, Greenberg, Papamakarios, Carpenter, Hoffman-Gelman, and several Mann/Connor dolphin-society works, but the supplied file appears to truncate the reference list (no entries past [55]). The data availability statement is missing: simulated data should be reproducible from code; the dolphin TSD surveillance data needs an explicit access statement (institutional repository, controlled-access pointer, or "available from the corresponding author on reasonable request, subject to data-use agreement with [institution]"). Both are PLOS submission requirements.
Suggested fix
Verify the reference list is complete in the submission file. Add a Data Availability Statement covering: (a) simulated data — link to the code repository with seed lists; (b) Shark Bay TSD data — institutional repository or DUA pointer; (c) any derived intermediate data files. PLOS requires these as a separate end-matter section, not buried in Methods.

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