{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T04:38:59Z","timestamp":1773463139096,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1010237","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,7,20]],"date-time":"2022-07-20T00:00:00Z","timestamp":1658275200000}}],"reference-count":48,"publisher":"Public Library of Science (PLoS)","issue":"7","license":[{"start":{"date-parts":[[2022,7,8]],"date-time":"2022-07-08T00:00:00Z","timestamp":1657238400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001711","name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","doi-asserted-by":"publisher","award":["200021 172578"],"award-info":[{"award-number":["200021 172578"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001711","name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","doi-asserted-by":"publisher","award":["200021 172578"],"award-info":[{"award-number":["200021 172578"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007479","name":"Fondazione Cassa di Risparmio di Padova e Rovigo","doi-asserted-by":"publisher","award":["55722"],"award-info":[{"award-number":["55722"]}],"id":[{"id":"10.13039\/100007479","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007479","name":"Fondazione Cassa di Risparmio di Padova e Rovigo","doi-asserted-by":"publisher","award":["55722"],"award-info":[{"award-number":["55722"]}],"id":[{"id":"10.13039\/100007479","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007479","name":"Fondazione Cassa di Risparmio di Padova e Rovigo","doi-asserted-by":"publisher","award":["55722"],"award-info":[{"award-number":["55722"]}],"id":[{"id":"10.13039\/100007479","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Special Integrative Fund for Research","award":["FISR-2020IP-04249"],"award-info":[{"award-number":["FISR-2020IP-04249"]}]},{"name":"Special Integrative Fund for Research","award":["FISR-2020IP-04249"],"award-info":[{"award-number":["FISR-2020IP-04249"]}]},{"name":"Special Integrative Fund for Research","award":["FISR-2020IP-04249"],"award-info":[{"award-number":["FISR-2020IP-04249"]}]},{"name":"Special Integrative Fund for Research","award":["FISR-2020IP-04249"],"award-info":[{"award-number":["FISR-2020IP-04249"]}]},{"name":"Special Integrative Fund for Research","award":["FISR-2020IP-04249"],"award-info":[{"award-number":["FISR-2020IP-04249"]}]},{"name":"Special Integrative Fund for Research","award":["FISR-2020IP-04249"],"award-info":[{"award-number":["FISR-2020IP-04249"]}]},{"DOI":"10.13039\/501100008904","name":"Universit\u00e0 Ca\u2019 Foscari di Venezia","doi-asserted-by":"publisher","award":["Fondi di primo insediamento"],"award-info":[{"award-number":["Fondi di primo insediamento"]}],"id":[{"id":"10.13039\/501100008904","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>While campaigns of vaccination against SARS-CoV-2 are underway across the world, communities face the challenge of a fair and effective distribution of a limited supply of doses. Current vaccine allocation strategies are based on criteria such as age or risk. In the light of strong spatial heterogeneities in disease history and transmission, we explore spatial allocation strategies as a complement to existing approaches. Given the practical constraints and complex epidemiological dynamics, designing effective vaccination strategies at a country scale is an intricate task. We propose a novel optimal control framework to derive the best possible vaccine allocation for given disease transmission projections and constraints on vaccine supply and distribution logistics. As a proof-of-concept, we couple our framework with an existing spatially explicit compartmental COVID-19 model tailored to the Italian geographic and epidemiological context. We optimize the vaccine allocation on scenarios of unfolding disease transmission across the 107 provinces of Italy, from January to April 2021. For each scenario, the optimal solution significantly outperforms alternative strategies that prioritize provinces based on incidence, population distribution, or prevalence of susceptibles. Our results suggest that the complex interplay between the mobility network and the spatial heterogeneities implies highly non-trivial prioritization strategies for effective vaccination campaigns. Our work demonstrates the potential of optimal control for complex and heterogeneous epidemiological landscapes at country, and possibly global, scales.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1010237","type":"journal-article","created":{"date-parts":[[2022,7,8]],"date-time":"2022-07-08T14:15:45Z","timestamp":1657289745000},"page":"e1010237","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":39,"title":["Optimal control of the spatial allocation of COVID-19 vaccines: Italy as a case study"],"prefix":"10.1371","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2677-6574","authenticated-orcid":true,"given":"Joseph Chadi","family":"Lemaitre","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6892-9826","authenticated-orcid":true,"given":"Damiano","family":"Pasetto","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5925-0440","authenticated-orcid":true,"given":"Mario","family":"Zanon","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5872-0666","authenticated-orcid":true,"given":"Enrico","family":"Bertuzzo","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1326-9992","authenticated-orcid":true,"given":"Lorenzo","family":"Mari","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7447-049X","authenticated-orcid":true,"given":"Stefano","family":"Miccoli","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5177-803X","authenticated-orcid":true,"given":"Renato","family":"Casagrandi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8063-9178","authenticated-orcid":true,"given":"Marino","family":"Gatto","sequence":"additional","affiliation":[]},{"given":"Andrea","family":"Rinaldo","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2022,7,8]]},"reference":[{"issue":"7805","key":"pcbi.1010237.ref001","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1038\/d41586-020-01063-8","article-title":"If a coronavirus vaccine arrives, can the world make enough?","volume":"580","author":"R Khamsi","year":"2020","journal-title":"Nature"},{"key":"pcbi.1010237.ref002","unstructured":"National Academies of Sciences aM Engineering. Framework for Equitable Allocation of COVID-19 Vaccine. Kahn B, Brown L, Foege W, Gayle H, editors. The National Academies Collection: Reports funded by National Institutes of Health. Washington (DC): National Academies Press (US); 2020. Available from: http:\/\/www.ncbi.nlm.nih.gov\/books\/NBK562672\/."},{"issue":"4","key":"pcbi.1010237.ref003","doi-asserted-by":"crossref","first-page":"766","DOI":"10.3390\/vaccines8040766","article-title":"Vaccination Criteria Based on Factors Influencing COVID-19 Diffusion and Mortality","volume":"8","author":"I Spassiani","year":"2020","journal-title":"Vaccines"},{"issue":"6","key":"pcbi.1010237.ref004","doi-asserted-by":"crossref","first-page":"eabf1374","DOI":"10.1126\/sciadv.abf1374","article-title":"Vaccine optimization for COVID-19: Who to vaccinate first?","volume":"7","author":"L Matrajt","year":"2020","journal-title":"Science Advances"},{"issue":"1","key":"pcbi.1010237.ref005","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1038\/s41591-020-01172-x","article-title":"Indirect benefits are a crucial consideration when evaluating SARS-CoV-2 vaccine candidates","volume":"27","author":"ME Gallagher","year":"2021","journal-title":"Nature Medicine"},{"key":"pcbi.1010237.ref006","first-page":"1","article-title":"Alternative dose allocation strategies to increase benefits from constrained COVID-19 vaccine supply","author":"AR Tuite","year":"2021","journal-title":"Annals of Internal Medicine"},{"issue":"4","key":"pcbi.1010237.ref007","doi-asserted-by":"crossref","DOI":"10.1073\/pnas.2019617118","article-title":"Retrospective analysis of the Italian exit strategy from COVID-19 lockdown","volume":"118","author":"V Marziano","year":"2021","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"pcbi.1010237.ref008","article-title":"Spread and dynamics of the COVID-19 epidemic in Italy: Effects of emergency containment measures","author":"M Gatto","year":"2020","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"1","key":"pcbi.1010237.ref009","doi-asserted-by":"crossref","first-page":"4264","DOI":"10.1038\/s41467-020-18050-2","article-title":"The geography of COVID-19 spread in Italy and implications for the relaxation of confinement measures","volume":"11","author":"E Bertuzzo","year":"2020","journal-title":"Nature Communications"},{"issue":"6509","key":"pcbi.1010237.ref010","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1126\/science.abe2803","article-title":"An ethical framework for global vaccine allocation","volume":"369","author":"EJ Emanuel","year":"2020","journal-title":"Science"},{"issue":"6518","key":"pcbi.1010237.ref011","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1126\/science.abe5938","article-title":"Understanding COVID-19 vaccine efficacy","volume":"370","author":"M Lipsitch","year":"2020","journal-title":"Science"},{"key":"pcbi.1010237.ref012","article-title":"Model-informed COVID-19 vaccine prioritization strategies by age and serostatus","author":"KM Bubar","year":"2021","journal-title":"Science"},{"key":"pcbi.1010237.ref013","article-title":"Optimizing age-specific vaccination","author":"MC Fitzpatrick","year":"2021","journal-title":"Science"},{"key":"pcbi.1010237.ref014","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1056\/NEJMoa2035389","article-title":"Efficacy and safety of the mRNA-1273 SARS-CoV-2 vaccine","volume":"384","author":"LR Baden","year":"2020","journal-title":"New England Journal of Medicine"},{"issue":"1","key":"pcbi.1010237.ref015","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1186\/s12916-021-01923-8","article-title":"Who should be prioritized for COVID-19 vaccination in China? 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