Which movement matrix changes a district-level projection, and by how much

Question: How have metapopulation and mobility-network epidemic models quantified the sensitivity of district-level outbreak projections to human movement data sources such as displacement and travel survey matrices?

Answer

Taken together, the retrieved literature quantifies this sensitivity almost exclusively through matrix-substitution experiments — holding transmission parameters fixed and swapping one movement representation for another — supplemented by variance decomposition (Morris screening, Sobol indices) when the matrix is treated as one input among many. The collective verdict is asymmetric rather than a single number. Output functionals that depend on the rank ordering of districts are consistently robust: empirical commuting-and-air-traffic matrices and a purely theoretical radiation model both yield effective distances that predict the relative order of epidemic onset across counties and states [9], and in a displacement-driven district network in Uganda, three very different transmissibility scenarios produced nearly identical projected cumulative case counts [19]. Output functionals that depend on magnitudes, absolute timing, or subgroup distributions are consistently fragile: coarsening mobile-phone mobility from fine to aggregated spatial units produced wide variation in epidemic size and invasion timing [1], re-operationalising mobility (units visited versus stay-put probability, static versus dynamic networks) shifted the inferred timing of mortality inequality emergence in Brazil [2], and replacing administrative connectivity with distance-derived district interaction matrices changed German influenza forecast skill in a horizon-dependent way [6]. Across these papers, displacement matrices are the least tested source: the only recent district-level application uses IOM Displacement Tracking Matrix flows to build a sparse, highly unequal, modular network and reports importation and export risk per district, but does not benchmark that network against census or survey alternatives [19].

Substituting the matrix while freezing epidemiology makes mobility look either decisive or irrelevant, depending on the output functional

Studies that swap only the movement layer and report epidemic size or invasion timing find large effects: three nested aggregation scales of the same mobile-phone records produced wide variation in projected epidemic size and spatial invasion timing, modulated by transmissibility and by whether the seeding district was urban [1]. Studies that swap only the movement layer and report ordering or relative quantities find the opposite, with effective distance predicting onset order under both empirical commuting and theoretical radiation matrices [9]. The disagreement is therefore largely definitional: rank-preserving properties of the matrix survive substitution, whereas quantities calibrated to the matrix's absolute off-diagonal mass do not.

Variance decomposition assigns movement flows a modest share of projection variance next to population structure

When mobility is entered as one input in a global sensitivity analysis, first-order Sobol indices show peak magnitude largely insensitive to a city's outbound and inbound flows when city sizes are comparable, with sensitivity shifting toward inbound flow only as size asymmetry grows [3]. In scaling analyses across seven diseases in Brazilian cities, population size exerts a greater influence on case counts than variation in the number of commuters [5]. Comparable decompositions in agent-based models locate most output variance in demographic inputs such as household-size and age distributions rather than in the mobility layer [14]. These rankings are conditional on the chosen priors and on evaluating mobility as scalar flow magnitudes rather than as network topology.

Displacement networks are analysed structurally and epidemiologically, but not comparatively

The Uganda Bundibugyo analysis is the clearest instance of a displacement-derived matrix entering a district-level metapopulation SEIR projection: 11,245 observed DTM movements over 135 districts and two DRC provinces yielded a network with density 0.11, Gini 0.67 and modularity 0.50, and identified single districts with dominant in-strength and out-strength, with Morris elementary-effects screening and total-order Sobol indices used for global sensitivity [19]. Its reported prediction-interval coverage of 0.80 against the early observed curve is the only calibration check, and the projection was not run with an alternative displacement or survey matrix, so the sensitivity of the district-level output to the source remains unquantified.

Data quality within a single source often matters more than the choice between sources

Trajectory sparsity in GPS-derived records causes substantial underestimation of epidemic intensity, and the bias depends on the structure of missingness rather than its volume alone; inverse-probability weighting of the contact network before calibration reduces both bias and parameter misspecification [10]. Converting aggregate mobility into contact rates naively is the least accurate of four tested approaches, with regression-based scaling substantially better even out of sample [7]. Mobility-derived synthetic contact matrices nonetheless outperformed empirical survey matrices in fitting French hospital admissions, while underestimating contacts for under-19s by a factor of 3.4 [8]. Which source "wins" thus depends on which target the model is scored against.

Representation choices inside the matrix can rival source choice: trip duration, directionality, and within-day movement

Treating transmission during travel explicitly rather than as instantaneous mixing significantly altered outbreak patterns in a German graph-ODE metapopulation [23]. Distinguishing visitor dynamics from indefinite-length migration changed inferred movement parameters and implied that competing migration models underestimate outbreak magnitude attributable to visitors [21]. Ignoring within-day movement biases location-specific and network-level reproduction numbers [24], and mobility-blind or mobility-misspecified inference produces biased reproduction ratios in spatially structured populations [4] [17]. Adding a network at all can be worth up to 25% improvement in peak prediction over isolated subnational models [16].

Conflicts and gaps

Two disagreements are unresolved. First, whether mobility data materially changes projections: wide variation in size and invasion timing under aggregation [1] and systematic shifts in inequality timing [2] sit against onset-order robustness [9] and flow-insensitivity of peaks [3]; no paper reports both classes of functional on one system. Second, mobility coefficients are structurally hard to identify from case data alone: Sobol-plus-Bayesian analysis shows diffusion coefficients require additional information beyond detected, critical and death counts [12], which means reported sensitivities are partly artefacts of the calibration design. Beyond this, no retrieved study performs a head-to-head district-level comparison of displacement (DTM), travel-survey, census commuting and call-detail-record matrices on identical districts, times and epidemiological parameters; the value of mobility data is also reported to depend on scenario type, adding most where travel is habitual and case counts are low and clustered [11], which makes single-setting sensitivity estimates non-transferable.

What would change the answer

A factorial benchmark on one district-level metapopulation, with the matrix treated as a four-level factor (DTM displacement, travel survey, census commuting, mobile-phone OD) crossed with epidemiological parameters, scored on a pre-registered panel of functionals — district onset rank correlation, peak height, peak week, and subgroup attack-rate ratios — using proper scoring rules such as the energy score rather than point error [15], would resolve the functional-dependence conflict. Pairing that with Bayesian joint estimation of a matrix scaling factor and reporting posterior coverage against held-out district trajectories, as the Uganda DTM model begins to do [19] and as gravity formulations do for onset times [13] [22], would separate matrix error from epidemiological confounding. District-level mobility covariates already fitted against two decades of surveillance across 670 districts [18], and air-traffic scenario ensembles that hold the network fixed while varying outbreak geography [20], supply the validation infrastructure; applying the sparsity correction before calibration [10] would prevent within-source data-quality artefacts from masquerading as between-source disagreement.

References

[1] Corgel, R., Grantz, K. H., Gardner, L. M., Cummings, D. A., De Silva, H., Somaratne, T., Silva, D., Fernando, L., Wesolowski, A.. "Characterizing the impact of incorporating spatially aggregated human mobility data into infectious disease models". medRxiv. 2025-11-28T00:00:00.000Z. URL: https://doi.org/10.1101/2025.11.26.25340802

[2] Jordan Klein. "Mobility measurement and network structure shape mortality inequalities in epidemic simulations". socarxiv. 2026-05-28T10:15:48.957Z. URL: https://osf.io/bu4h9_v1

[3] Klochkov, K. A., Kozlov, I. E., Ilina, E. N., Manolov, A. I.. "Transportation flows and outbreak origins in epidemic spread: Insights from agent-based modeling". medRxiv. 2025-10-13T00:00:00.000Z. URL: https://doi.org/10.1101/2025.10.09.25337674

[4] Piero Birello, Michele Re Fiorentin, Boxuan Wang, Vittoria Colizza, Eugenio Valdano. "Estimates of the reproduction ratio from epidemic surveillance may be biased in spatially structured populations". arxiv. 2025-01-08T00:00:00.000Z. URL: https://doi.org/10.1038/s41567-024-02471-7

[5] Nathalia A. Loureiro, Camilo R. Neto, Jack Sutton, Matjaz Perc, Haroldo V. Ribeiro. "Impact of inter-city interactions on disease scaling". arxiv. 2025-01-06T00:00:00.000Z. URL: https://doi.org/10.1038/s41598-024-84252-z

[6] Stapper, M., Funk, S.. "Fine-Grid Spatial Interaction Matrices for Surveillance Models, with Application to Influenza in Germany". medRxiv. 2025-07-04T00:00:00.000Z. URL: https://doi.org/10.1101/2025.04.03.25325159

[7] Prestige, E., Coletti, P., Backer, J. A., Davies, N. J., Edmunds, W. J., Jarvis, C. I.. "Estimating social contact rates for the COVID-19 pandemic using Google mobility and pre-pandemic contact surveys". medRxiv. 2025-03-25T00:00:00.000Z. URL: https://doi.org/10.1101/2023.12.19.23300209

[8] Di Domenico, L., Bosetti, P., Sabbatini, C. E., Opatowski, L., Colizza, V.. "Mobility-driven synthetic contact matrices: a scalable solution for real-time pandemic response modeling". medRxiv. 2025-09-30T00:00:00.000Z. URL: https://doi.org/10.1101/2024.12.12.24318903

[9] Pandey, A., Zhong, L., Rennert, L.. "Mobility-informed metapopulation models predict the spatio-temporal spread of respiratory epidemics across scales". medRxiv. 2025-06-26T00:00:00.000Z. URL: https://doi.org/10.1101/2025.06.26.25330297

[10] Federico Delussu, Francisco Barreras, Yuan Liao, Duncan J. Watts, Laura Alessandretti. "Empirical Trajectory Sparsity Biases Mobility-Informed Epidemic Modeling". arxiv. 2026-09-24T00:00:00.000Z. URL: https://arxiv.org/abs/2605.31282

[11] Cameron Zachreson, Lewis Mitchell, Michael J. Lydeamore, Nicolas Rebuli, Martin Tomko, Nicholas Geard. "Risk mapping for COVID-19 outbreaks in Australia using mobility data". arxiv. 2026-09-21T00:00:00.000Z. URL: https://doi.org/10.1098/rsif.2020.0657

[12] Olga Krivorotko, Tatiana Zvonareva, Andrei Neverov. "Identifiability of the spatial SEIR-HCD model of COVID-19 propagation". arxiv. 2024-12-30T00:00:00.000Z. URL: https://arxiv.org/abs/2412.18858

[13] Couture, A., Biggerstaff, M., Sheppard, M., Budd, A., Kite-Powell, A., Morris, S.. "Spatiotemporal Transmission of Influenza in the US during the 2022/23 Season". medRxiv. 2025-07-11T00:00:00.000Z. URL: https://doi.org/10.1101/2025.07.10.25331274

[14] Tsurkis, V., Kozlov, I., Samoilov, A., Maslova, I., Ilina, E., Lukashev, A., Manolov, A.. "Demographic Drivers of Epidemic Outcomes: Sensitivity Analysis of Multidimensional Parameters in the Covasim Model". medRxiv. 2025-10-17T00:00:00.000Z. URL: https://doi.org/10.1101/2025.10.14.25328629

[15] Bay, C., Mu, K., St-Onge, G., Chinazzi, M., Davis, J. T., Vespignani, A.. "Evaluation of stochastic trajectory-based epidemic models using the energy score". medRxiv. 2025-08-18T00:00:00.000Z. URL: https://doi.org/10.1101/2025.01.13.25320493

[16] Aalto, A., Proverbio, D., Giordano, G., Skupin, A., Goncalves, J.. "Networked SIRS model with Kalman filter state estimation for epidemic monitoring in Europe". medRxiv. 2025-02-07T00:00:00.000Z. URL: https://doi.org/10.1101/2025.02.06.25321780

[17] Roy, M., Clapham, H. E., Mishra, S.. "Incorporating human mobility to enhance epidemic response and estimate real-time reproduction numbers". medRxiv. 2025-10-03T00:00:00.000Z. URL: https://doi.org/10.1101/2025.04.25.25326411

[18] Fletcher, C., Belman, S., Do, K. Q., Pham, Q. D., Nguyen, T. T. T., Gibb, R., Lan, P. T., Tu, T. C., Tuan, N. H., Lührsen, D., Tsarouchi, G., Harpham, Q., Colon-Gonzalez, F. J., Palmer, J. R. B., Lowe, R.. "Compound climate extremes, socioeconomic conditions and human mobility influence dengue dynamics heterogeneously across Vietnam". medRxiv. 2026-09-21T00:00:00.000Z. URL: https://doi.org/10.64898/2026.09.19.26363468

[19] Walekhwa, A. W., Mbaka, P., Nannyonga, B. K., Silal, S. P., Bbuye, M., Magoba, B., Nakiire, L., Lamorde, M., Sulaimon, T. A., Kwesiga, B., Sabiiti, W., Mutamba, W., Turinawe, G., Nakazibwe, B., Kayiwa, J., Nantongo, M., Ipola, P. A., Kungu, P., Ario, A. R., Kagirita, A., Lubwama, B., Kirenga, B. J., Wayengera, M., Muruta, A. N., Olaro, C., Atwine, D.. "Exploratory network-based modelling of Bundibugyo Ebola virus disease importation and spread in Uganda using Displacement Tracking Matrix flow data". medRxiv. 2026-10-19T00:00:00.000Z. URL: https://doi.org/10.64898/2026.06.22.26356210

[20] Fanelli, F., Parino, F., Poletto, C., Colizza, V.. "Shifting patterns of importation risk of Bundibugyo Ebola virus disease to Europe under outbreak expansion scenarios". medRxiv. 2026-06-04T00:00:00.000Z. URL: https://doi.org/10.64898/2026.05.31.26354511

[21] Soewongsono, A. C., Thompson, A., Landis, M. J.. "Inferring epidemiological parameters under an infectious phylogeography model with visitor dynamics". medRxiv. 2025-12-18T00:00:00.000Z. URL: https://doi.org/10.64898/2025.12.16.25342415

[22] Chen, S., Bento, A. I.. "Multiscale Modelling Reveals Accelerating Community Outbreak Risks of Measles in the United States". medRxiv. 2026-01-30T00:00:00.000Z. URL: https://doi.org/10.64898/2026.01.27.26345010

[23] Zunker, H., Schmieding, R., Kerkmann, D., Schengen, A., Meyer-Hermann, M., Diexer, S., Mikolajczyk, R., Kuehn, M. J.. "Novel travel time aware metapopulation models and multi-layer waning immunity for late-phase epidemic and endemic scenarios". medRxiv. 2024-10-28T00:00:00.000Z. URL: https://doi.org/10.1101/2024.03.01.24303602

[24] Cathal Mills, Benjamin Reddy, William S. Hart, Robin N. Thompson, Kris V. Parag, Moritz U. G. Kraemer, Christl A. Donnelly, Ben Lambert. "Multi-scale measures of time-varying epidemic spread on human mobility networks". arxiv. 2026-07-31T00:00:00.000Z. URL: https://arxiv.org/abs/2607.28514

How this survey was made

This survey answers one question: “How have metapopulation and mobility-network epidemic models quantified the sensitivity of district-level outbreak projections to human movement data sources such as displacement and travel survey matrices?”

We keep our own collection of recent preprints and refresh it every day from bioRxiv, medRxiv, arXiv, PsyArXiv, SocArXiv and ChemRxiv. For each survey, we search that collection for recent work and keep the strongest matches: papers that use the same terms as the question, and papers on the same topic in different words.

The text was written from the titles and abstracts of those papers; the full texts were not read. Statements that draw on a particular paper are marked with a number in brackets. The reference list just above is the 24 papers whose work this text draws on, chosen from the 93 papers those searches returned; the rest of the shortlist is not printed. It is not a complete review of everything published on the question.

Treat this as a starting point and a reading list, not a peer-reviewed review. The searches behind this survey ran on October 21, 2026 and covered work from the previous two years.