Pooling air, commuting and other mobility layers into one travel map may preserve the scale of extreme importation events while obscuring the route or transport mode behind them, according to an arXiv version 1 preprint dated 26 August 2026. The paper asks which features of directed, multilayer mobility survive pooling and which become nonidentifiable, including what that loss could mean for epidemic surveillance.
In ordinary terms, the theory separates the size of a shock from its direction. Sampling and adding nonnegative flows preserve the radial tail index—the mathematical measure of how often exceptionally large importations occur—but they can reweight the angular pattern of routes and merge distinctions that the pooled data no longer contain. The result depends on explicit regular-variation, independence, positivity and moment assumptions.
When route detail can survive
The paper gives a sharp boundary for recoverability. Route composition can be inferred from the aggregate pattern exactly when the normalized signatures of the routes are affinely independent—in practical terms, when none can be rebuilt as a weighted combination of the others. If all layers are collapsed to one aggregate coordinate, the mapping is one-to-one only when there is a single route. Pooling can therefore be enough for total importation, hotspot ranking or arrival time without being enough to identify which mode carried an importation.
What the simulations exposed
To examine the consequences in an epidemic model, the researchers built synthetic multiplex networks with 60 regions and ran epidemic simulations for 110 days. For mechanism-removal comparisons, they used 300 paired stochastic replicates with common random numbers and paired bootstrap intervals, allowing corresponding model outputs to be compared under the same random variation.
In those paired comparisons, population-alignment removal corresponded to a 13.98-day difference in secondary-invasion timing and a 7.16-region difference in spread by day 110. Gateway-alignment removal corresponded to differences of 5.71 days and 2.56 regions. The timing result depended on hub seeding and was close to zero in additional networks seeded at median-population or random locations.
The full synthetic multiplex also showed how aggregate burden can coexist with a concentrated but uncertain route backbone. In the median replicate, 87.5 infectious routes were active and 454 exposures were imported. Among upper-quartile outbreaks, route entropy—a measure of how spread out route contributions are—was 3.06 nats, and the dominant-route share was 0.395. Bootstrap 95% intervals were 3.03–3.10 for entropy and 0.390–0.401 for dominant-route share.
That concentration had a practical consequence in a synthetic surveillance exercise. With a budget of 10 destinations, targeting based on layer-resolved data covered 46.5% of the network’s air-import burden, compared with 38.3% when the layers were pooled—a difference of 8.2 percentage points. The paired bootstrap interval for that pooling regret was 7.6 to 8.9 points.
A separate constructed twin made the identification problem more stark. Across 200 replicates, two decompositions had air shares of 13.1% and 14.9%, but their top-ten air-surveillance destinations overlapped in only five of 10 places. The Jaccard overlap, a standard measure of set similarity, was 0.33, with a range of 0.33 to 0.43 across surveillance budgets. Because the twin was constructed under a shared-coupling model, it illustrates a conditional ambiguity rather than a universal pattern.
The regional evidence
For the empirical checks, the researchers fit a discrete-time first-invasion hazard: a model of the chance that a region experiences its first invasion at a given time. They compared constant-only, timing-only, air-only, commuting-only and full specifications, then refit the models while leaving each target region out. The authors treat these outputs as model-based reconstructions, not intervention or causal estimates.
In the US pandemic-influenza reconstruction, the data covered 369 metropolitan statistical areas, 15 weeks of ILI+ incidence and 215 non-seed onset targets. Air mobility added 5.2 log-likelihood units—a measure of fitted information—beyond commuting, while target-excluded onset error fell from 0.70 to 0.61 weeks under the full specification. Fitted air attribution was 11.6%. At a 10-destination surveillance budget, layer-resolved rankings covered 56.2% of fitted air burden, versus 45.4% for pooled rankings—a 10.8-point loss, with an interval of 2.2 to 49.0 points.
Italy produced a different fitted picture. The onset reconstruction covered 21 NUTS-2 regions and 19 non-seed targets, while structural comparisons used 110 finer NUTS-2010 level-3 units. Commuting added 5.24 log-likelihood units beyond the national epidemic curve, and the full model’s negative log likelihood was 51.48, compared with 56.72 for timing only. Target-excluded mean absolute error was 3.05 days for the full model versus 4.74 days for timing only. The maximum-likelihood air coefficient was zero, but that does not establish that air-mediated spread was absent.
Across 2,000 reconstructed Italian networks, external risk accounted for 52.0% of post-seed introductions, commuting for 47.5% and air for 0.4%; the replicate-level air-share interval ran from 0 to 5.3%. The paper does not treat the US and Italian estimates as a controlled cross-setting comparison.
A warning about pooled maps
The authors’ central warning is about the kind of question a mobility map can answer. A pooled map may help rank overall importation burden or estimate arrival timing, yet it can point surveillance toward a different set of destinations when the task is to follow air-specific risk. The study does not show that pooled data always fail, that multilayer structure universally accelerates invasion, or that fitted route probabilities are the true routes; it shows that route and mode attribution can be lost under pooling.
The document is an arXiv version 1 preprint dated 26 August 2026, and the work received support from three named Chinese funding programs.
Paper data and sources
Original title: Pooling Mobility Obscures Epidemic Invasion Routes
Authors: Tiandong Wang, Wei Yang
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text