{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T22:46:53Z","timestamp":1787870813469,"version":"build-2784847793"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,7,6]],"date-time":"2026-07-06T00:00:00Z","timestamp":1783296000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,7,6]],"date-time":"2026-07-06T00:00:00Z","timestamp":1783296000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e.V. (DLR)"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    In times of epidemics, swift reaction is necessary to mitigate epidemic spreading. For this reaction, localized approaches have several advantages, limiting necessary resources and reducing the impact of interventions on a larger scale. However, training a separate machine learning (ML) model on a local scale is often not feasible due to limited available data. Centralizing the data is also challenging because of its high sensitivity and privacy constraints. In this study, we consider a localized strategy based on the German counties and communities managed by the related local health authorities (LHA). For the preservation of privacy to not oppose the availability of detailed situational data, we propose a privacy-preserving forecasting method that can assist public health experts and decision makers. ML methods with federated learning (FL) train a shared model without centralizing raw data. Considering the counties, communities or LHAs as clients and finding a balance between utility and privacy, we study a FL framework with client-level differential privacy (DP). We train a shared multilayer perceptron on sliding windows of recent case counts to forecast the number of cases in the future, while clients exchange only norm-clipped updates and the server aggregates updates with DP noise. We evaluate the approach on COVID-19 data on county-level during two phases: November 2020 and March 2022 (Omicron). As expected, very strict privacy (\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\varepsilon \\le 0.5$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ) yields unstable, unusable forecasts. At a moderately strong but still privacy-preserving level (\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\varepsilon = 2$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ), the DP model closely approaches the non-DP model:\n                    <jats:inline-formula>\n                      <jats:tex-math>$$R^2\\approx 0.93$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    (vs. 0.96) and mean absolute percentage error (MAPE)\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\approx 26\\%$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    in November 2020;\n                    <jats:inline-formula>\n                      <jats:tex-math>$$R^2\\approx 0.85$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    (vs. 0.90) and MAPE\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\approx 24\\%$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    in March 2022. Overall, our results support the feasibility of privacy-preserving collaboration among health authorities for local forecasting. In the evaluated COVID-19 phases, client-level DP-FL delivered useful county-level predictions with formal privacy guarantees under the stated threat model. The appropriate privacy budget should nevertheless be re-evaluated for other epidemic phases and applications.\n                  <\/jats:p>","DOI":"10.1038\/s41598-026-60725-1","type":"journal-article","created":{"date-parts":[[2026,7,6]],"date-time":"2026-07-06T21:14:33Z","timestamp":1783372473000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Differentially private federated learning for localized control of infectious disease dynamics"],"prefix":"10.1038","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1458-7805","authenticated-orcid":false,"given":"Raouf","family":"Kerkouche","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9825-365X","authenticated-orcid":false,"given":"Henrik","family":"Zunker","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8949-9896","authenticated-orcid":false,"given":"Mario","family":"Fritz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0906-6984","authenticated-orcid":false,"given":"Martin J.","family":"K\u00fchn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,7,6]]},"reference":[{"key":"60725_CR1","doi-asserted-by":"publisher","first-page":"14384","DOI":"10.1038\/s41598-024-64864-1","volume":"14","author":"J Mohring","year":"2024","unstructured":"Mohring, J. et al. Estimating the COVID-19 prevalence from wastewater. Sci. Rep. 14, 14384. https:\/\/doi.org\/10.1038\/s41598-024-64864-1 (2024).","journal-title":"Sci. Rep."},{"key":"60725_CR2","doi-asserted-by":"publisher","first-page":"3463","DOI":"10.1038\/s41467-024-47556-2","volume":"15","author":"S Merkt","year":"2024","unstructured":"Merkt, S. et al. Long-term monitoring of SARS-CoV-2 seroprevalence and variants in Ethiopia provides prediction for immunity and cross-immunity. Nat. Commun. 15, 3463. https:\/\/doi.org\/10.1038\/s41467-024-47556-2 (2024).","journal-title":"Nat. Commun."},{"key":"60725_CR3","doi-asserted-by":"publisher","first-page":"981","DOI":"10.3390\/v17070981","volume":"17","author":"Y Kheifetz","year":"2025","unstructured":"Kheifetz, Y., Kirsten, H., Schuppert, A. & Scholz, M. Modeling the complete dynamics of the SARS-CoV-2 pandemic of Germany and its federal states using multiple levels of data. 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