{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T20:17:29Z","timestamp":1770754649289,"version":"3.50.0"},"reference-count":28,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,11]],"date-time":"2022-04-11T00:00:00Z","timestamp":1649635200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/50008\/2020"],"award-info":[{"award-number":["UIDB\/50008\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/04106\/2020"],"award-info":[{"award-number":["UIDB\/04106\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>A fractional-order compartmental model was recently used to describe real data of the first wave of the COVID-19 pandemic in Portugal [Chaos Solitons Fractals 144 (2021), Art. 110652]. Here, we modify that model in order to correct time dimensions and use it to investigate the third wave of COVID-19 that occurred in Portugal from December 2020 to February 2021, and that has surpassed all previous waves, both in number and consequences. A new fractional optimal control problem is then formulated and solved, with vaccination and preventive measures as controls. A cost-effectiveness analysis is carried out, and the obtained results are discussed.<\/jats:p>","DOI":"10.3390\/axioms11040170","type":"journal-article","created":{"date-parts":[[2022,4,12]],"date-time":"2022-04-12T00:23:11Z","timestamp":1649722991000},"page":"170","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Fractional Modelling and Optimal Control of COVID-19 Transmission in Portugal"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5153-4879","authenticated-orcid":false,"given":"Silv\u00e9rio","family":"Rosa","sequence":"first","affiliation":[{"name":"Department of Mathematics, Instituto de Telecomunica\u00e7\u00f5es (IT), Universidade da Beira Interior, 6201-001 Covilh\u00e3, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8641-2505","authenticated-orcid":false,"given":"Delfim F. M.","family":"Torres","sequence":"additional","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,11]]},"reference":[{"key":"ref_1","unstructured":"(2021, July 07). World Health Organization. Available online: https:\/\/www.who.int\/emergencies\/diseases\/novel-coronavirus-2019\/interactive-timeline#."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Agarwal, P., Nieto, J.J., Ruzhansky, M., and Torres, D.F.M. (2021). 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