{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T20:01:07Z","timestamp":1785787267892,"version":"3.56.0"},"reference-count":59,"publisher":"National Academy of Sciences","issue":"32","license":[{"start":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T00:00:00Z","timestamp":1785715200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002347","name":"Bundesministerium f\u00fcr Forschung, Technologie und Raumfahrt","doi-asserted-by":"publisher","award":["031L0300A"],"award-info":[{"award-number":["031L0300A"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002347","name":"Bundesministerium f\u00fcr Forschung, Technologie und Raumfahrt","doi-asserted-by":"publisher","award":["031L0298"],"award-info":[{"award-number":["031L0298"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["2067\/1-390729940"],"award-info":[{"award-number":["2067\/1-390729940"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010434","name":"'la Caixa' Foundation","doi-asserted-by":"publisher","award":["LCF\/BQ\/PI23\/11970039"],"award-info":[{"award-number":["LCF\/BQ\/PI23\/11970039"]}],"id":[{"id":"10.13039\/100010434","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2026,8,11]]},"abstract":"<jats:p>\n                    Mitigation measures are essential for controlling the spread of infectious diseases during pandemics and epidemics, but they impose considerable societal, individual, and economic costs. We developed a general framework that combines simulation of disease dynamics with optimal control to determine mitigation strategies that balance infection and mitigation costs. Optimizing this trade-off, we identified three surprising effects: first, assuming a constant reproduction number\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:msub>\n                          <mml:mi>R<\/mml:mi>\n                          <mml:mn>0<\/mml:mn>\n                        <\/mml:msub>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    , the optimal response is typically \u201call-or-nothing\u201d: depending on disease severity, either strict mitigation or none at all is optimal, with intermediate levels emerging only in restricted regimes that we characterize analytically. Second, under seasonal variations, optimal mitigation is stricter during winter. Interestingly, a single wave of infections still arises in spring, replacing the autumn\/winter waves known for classical influenza. Third, during steady vaccination campaigns, even optimal mitigation can result in transient infection waves. Finally, we quantify the cost of delayed mitigation onset and show that even short delays can substantially increase total costs\u2014if the disease is severe. Overall, our framework is easily applicable to general and complex settings and thereby presents a versatile tool to explore optimal mitigation strategies for endemic and pandemic infectious disease.\n                  <\/jats:p>","DOI":"10.1073\/pnas.2527395123","type":"journal-article","created":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T19:06:16Z","timestamp":1785783976000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":0,"title":["Optimizing infectious disease mitigation under dynamic conditions"],"prefix":"10.1073","volume":"123","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-2606-1117","authenticated-orcid":false,"given":"Laura","family":"M\u00fcller","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/0087djs12","id-type":"ROR","asserted-by":"publisher"}],"name":"Max-Planck-Institute for Dynamics and Self-Organization","place":["G\u00f6ttingen, Germany"]},{"id":[{"id":"https:\/\/ror.org\/01y9bpm73","id-type":"ROR","asserted-by":"publisher"}],"name":"Institute for the Dynamics of Complex Systems, University of G\u00f6ttingen","place":["G\u00f6ttingen, Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fabio","family":"Sartori","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/0087djs12","id-type":"ROR","asserted-by":"publisher"}],"name":"Max-Planck-Institute for Dynamics and Self-Organization","place":["G\u00f6ttingen, Germany"]},{"id":[{"id":"https:\/\/ror.org\/04t3en479","id-type":"ROR","asserted-by":"publisher"}],"name":"Chair of Sociology and Computational Social Science, Karlsruhe Institute, Karlsruhe Institute of Technology","place":["Karlsruhe, Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jonas","family":"Dehning","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/0087djs12","id-type":"ROR","asserted-by":"publisher"}],"name":"Max-Planck-Institute for Dynamics and Self-Organization","place":["G\u00f6ttingen, Germany"]},{"id":[{"id":"https:\/\/ror.org\/01y9bpm73","id-type":"ROR","asserted-by":"publisher"}],"name":"Institute for the Dynamics of Complex Systems, University of G\u00f6ttingen","place":["G\u00f6ttingen, Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maximilian F.","family":"Eggl","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02gfc7t72","id-type":"ROR","asserted-by":"publisher"}],"name":"Institute of Neuroscience, Consejo Superior de Investigaciones Cient\u00edficas - Universidad de Miguel Hernandez","place":["Alicante, Spain"]},{"id":[{"id":"https:\/\/ror.org\/041nas322","id-type":"ROR","asserted-by":"publisher"}],"name":"Institute of Experimental Epileptology and Cognition Research, University of Bonn Medical Center","place":["Bonn, Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8905-5873","authenticated-orcid":false,"given":"Viola","family":"Priesemann","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/0087djs12","id-type":"ROR","asserted-by":"publisher"}],"name":"Max-Planck-Institute for Dynamics and Self-Organization","place":["G\u00f6ttingen, Germany"]},{"id":[{"id":"https:\/\/ror.org\/01y9bpm73","id-type":"ROR","asserted-by":"publisher"}],"name":"Institute for the Dynamics of Complex Systems, University of G\u00f6ttingen","place":["G\u00f6ttingen, Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2026,8,3]]},"reference":[{"key":"e_1_3_4_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11079-021-09638-2"},{"key":"e_1_3_4_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.psychres.2020.113419"},{"key":"e_1_3_4_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(78)90023-8"},{"key":"e_1_3_4_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-022-04720-5"},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-021-23761-1"},{"key":"e_1_3_4_6_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-021-24872-5"},{"key":"e_1_3_4_7_2","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.abg2243"},{"key":"e_1_3_4_8_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.abd9338"},{"key":"e_1_3_4_9_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-021-82873-2"},{"key":"e_1_3_4_10_2","doi-asserted-by":"publisher","DOI":"10.1186\/s12879-014-0695-9"},{"key":"e_1_3_4_11_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.abb9789"},{"key":"e_1_3_4_12_2","doi-asserted-by":"crossref","unstructured":"N. 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