feat(patch): meta-population model over the three affected provinces

[seabbs-bot]

Makes the headline model a meta-population: a renewal equation per province (Ituri, Nord-Kivu, Sud-Kivu) coupled by importation, with every national stream fitted against the summed provinces. n_patches defaults to 1, which collapses it onto the previous single-population model, so there is one model rather than two. Adds the per-province data to fit it.

What was wrong, and the fix

The national outbreak size depended on how many provinces the country was split into. Splitting adds no national data, so it must not. Like-for-like on 13 July the patch fit gave C_T 13,213 [10,390–18,963] against main's ~4,700 [3,455–7,051] — non-overlapping 90% intervals.

Three structural asymmetries caused it, all visible in the prior, before any data. All three are fixed.

1. Aggregation, much the largest. The deviations are centred unweighted, so mu(t) — the trend the molecular clock constrains — is the geometric mean of the provincial reproduction numbers, while the epidemic runs at the force-weighted arithmetic mean that implied_national_Rt recovers and the chain reports as R_T. Arithmetic exceeds geometric, so the country grew faster than its own trend, and the excess was spent in the pre-surveillance window where no counts contradict it. Measured at the prior, the aggregate exceeded the trend by 7.5% at the median — exactly the observed posterior shift, R_T 1.22 → 1.31, a ratio of 1.074.

The sign was forced by the data: Ituri carries ~90% of the force and Sud-Kivu is frozen at 3 confirmed cases across every vintage, so the compositions push the small provinces below trend and unweighted centring pushes Ituri above it.

The renewal is now anchored: each day every province is scaled by one common factor so the implied national reproduction number is mu(t) exactly. The deviations become pure contrasts and the national level is left to mu alone, which is what the model already claimed. The ratios between provinces, which is what the composition data identify, are untouched.

2. Importation manufactured infections rather than moving them. The destination gained eps * K * I_prev and the origin lost nothing, so every patch's total rose and none fell. It now debits the origin exactly what the destinations are credited.

3. Seeding scaled with the patch count. The fractions added to the national cryptic seed instead of partitioning it, silently redefining 2^m from the country's cryptic size — which is what the m prior is elicited as — to Ituri's. They now partition it.

Result. With the same trend and the same total seed, three provinces reproduce the single-population national trajectory to machine precision, day by day, with importation live and heterogeneous deviations. On the test setup the old code inflated the national cumulative total roughly thirtyfold; it is now exact.

The invariant is pinned deterministically rather than by comparing prior medians — the prior on C_T is heavy-tailed enough that its median is dominated by sampling noise, which is why this was not caught earlier.

The comparison was also not controlled. The headline fit and sens_no_patches are the two halves of this sensitivity, so they must differ only in the patch structure. They had drifted apart by nine keyword arguments. genetic defaults to nothing, so the headline was silently running with no genetic TMRCA likelihood while the control had one. Measured, that term is a soft one-sided penalty: nonzero on 31 of 40 prior draws, up to ~1.1 log units against a total log-density of ~12,100 — necessary for the comparison to be controlled, but weak, and not on its own an explanation for the gap. Both specs now splat one shared configuration.

Still open: the fit does not fit the CI budget

Three provinces cost about twice as much per draw as one. Measured:

	parameters	gradient
1 patch	140	26.2 ms
3 patches	220	53.0 ms

That is a factor of 2.03, and the extra dimensions lengthen NUTS trajectories on top of it. The single-patch fit takes 314 minutes at 500 draws, so three patches at 500 needs on the order of 700, against the timeout-minutes: 350 budget on the fit job. Both 800 and 500 draws were duly cancelled at that mark without finishing, so the documentation has never rendered on this branch.

Set to 200 draws, which should land near 280 minutes. That is half what every other fit in the matrix uses, so the headline would have half the effective sample size of its own sensitivities. Raising the timeout is not an option — GitHub's ceiling is 360. The real alternatives are a runner without that ceiling, or a cheaper patch model. Worth a decision rather than my quiet choice.

Consequently no posterior fit of the corrected model exists yet. Every number above is deterministic or prior-predictive. The control to compare against is sens_no_patches at C_T 8,625 [6,391–13,126], which is unaffected by the fixes: at one patch the anchoring factor is exactly 1.0 on every day of every draw and no seed fraction is sampled, so that path is bit-identical to before.

The model

Provincial reproduction numbers are the national weekly-knot walk plus deviations that sum to zero, drawn from a correlated random walk:

log R_{p,t} = mu(t) + delta_p(t),        sum_p delta_p(t) = 0
Delta delta(t_k) ~ MVN(0, Sigma),        Sigma = diag(sigma) . Omega . diag(sigma)

mu(t) is the existing national walk and is the pooling target. sigma_delta is sampled, so whether the provinces share one temporal shape is estimated rather than assumed; sigma_delta -> 0 recovers a fixed ratio between them. The national R_T is backed out by inverting the renewal equation on the summed infections, which is the force-of-infection-weighted mean of the provincial Rts.

The split is identified by the deaths. A province's case count is the product of its incidence and its case-finding, and only the product is observed; the tests-analysed denominator cancels out of the normalised shares. The case-fatality ratio and the death-confirmation probability belong to the virus and to a national laboratory rather than to a province, so they cancel out of the normalised death shares. The death split identifies the incidence split and the case split then identifies ascertainment as the residual. Both are scored as compositions conditional on the national total, so neither re-scores data the national streams already carry.

Connectivity is a structural assumption. There is no mobility data, so the kernel is a fixed weighting by destination population with a sampled intensity, weakly identified against the secondary-province seeds.

Data

• [province_confirmed_history], [province_death_history] — per-province cumulative confirmed cases and deaths from Tableau 1 (20 vintages), scanned by scripts/scan_province_tableau1.jl.
• [province_lab_daily_history] — per-province laboratory throughput (18 vintages), scanned by scripts/scan_province_lab.jl.

Both scans are gated on reconciling exactly with the national totals on every date.

Reporting

The spatial section previously stacked every province against every quantity in one twenty-one-row table, and never showed provincial Rt over time — the question the model exists to answer. Now:

• a cross-province overview, one row per province;
• the reproduction number by province over time, faceted, with the national trajectory behind each panel;
• one detail table per province;
• the importation intensity reported alongside the kernel it scales.

The trajectory is rebuilt by reconstruct_patch_rt from the deviation knots the chain now carries as delta_knots, and a test pins that reconstruction against the model's own R_T_patch so the panels cannot drift from the tables.

Other changes in this round

• Rebased on main.
• The release notes were filed under a second ## v1.13.0 heading, a version already released. Moved to v1.14.0 and bumped the version.

Review

The anchoring is the change worth arguing about. test/test_patch_model.jl explicitly rejected reference coding (delta_1 = 0) as an identifiability artefact and chose unweighted centring instead; anchoring keeps the sum-to-zero deviations exactly as they were and fixes the aggregation at the renewal instead, so no province is privileged and mu recovers its stated meaning. If you would rather fix it by centring on incidence weights, that is the alternative and it is a smaller change to the maths but a larger one to the interpretation of delta.

This was opened by a bot. Please ping @seabbs for any questions.

[seabbs-bot]

Review pass done (4 inline comments above). CI status: pre-commit, Downgrade compat (Julia 1.11), Julia lts - ubuntu-latest, Resolve env and list fits and Fit exports all pass; the remaining Julia matrix jobs and the 11-job fit matrix are still running. No failures so far.

One further observation from watching the fit matrix fan out: bvd_patch_joint is not in the fits registry. The matrix runs joint, cases, deaths, confirmed, confirmed_deaths, exports, treatment, and the frozen vintages — no patch entry. grep -rn patch scripts/run.jl scripts/reproduce.jl returns nothing, and nothing under scripts/ constructs a bvd_patch_joint.

So the patch model has unit tests (test/test_patch_model.jl, which exercise the renewal primitives and the submodel varnames) but is never fit end-to-end in CI, produces no release artefact, and appears on no docs/analysis page. For a draft that is a reasonable place to be, but it means the two critical issues I flagged above — the secondary-patch seed prior, and the unused per-province lab denominator — would not have been caught by anything in the pipeline. Registering a patch fit (even a short, low-draw one) is what would turn the posterior-predictive check into a standing gate rather than a one-off manual run.

This was opened by a bot. Please ping @seabbs for any questions.

[codecov]

Codecov Report

❌ Patch coverage is 92.40987% with 40 lines in your changes missing coverage. Please review.
✅ Project coverage is 93.64%. Comparing base (536fa1a) to head (5ad91fd).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/plots.jl	39.34%	37 Missing ⚠️
src/models/joint.jl	96.73%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #412      +/-   ##
==========================================
- Coverage   93.93%   93.64%   -0.30%     
==========================================
  Files          15       16       +1     
  Lines        3464     3949     +485     
==========================================
+ Hits         3254     3698     +444     
- Misses        210      251      +41     

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[github-actions]

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View the docs for this PR at: http://epiforecasts.io/BVDOutbreakSize/previews/PR412/

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[seabbs]

This needs to be the new headline model ie joint and be wired into the analysis and sensitivity ie for one week ahead forecasts. I don't see evidence it works here

[seabbs]

There are some conflicts. The much larger outbreak size is worrying and I am not sure plausible. You don't show estimates or forecats for any of the spatial patches or Rt by patch