{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T22:12:13Z","timestamp":1761948733543,"version":"3.37.3"},"reference-count":18,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MBE"],"published-print":{"date-parts":[[2021]]},"abstract":"<jats:p xml:lang=\"fr\">&lt;abstract&gt;&lt;p&gt;In this work we use simple mathematical models to study the impact of vaccination against COVID-19 in Portugal. First, we fit a SEIR type model without vaccination to the Portuguese data on confirmed cases of COVID-19 by the date of symptom onset, from the beginning of the epidemic until the 23rd January of 2021, to estimate changes in the transmission intensity. Then, by including vaccination in the model we develop different scenarios for the fade-out of the non pharmacological intervention (NPIs) as vaccine coverage increases in the population according to Portuguese vaccination goals. We include a feedback function to mimic the implementation and relaxation of NPIs, according to some disease incidence thresholds defined by the Portuguese health authorities.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/mbe.2022043","type":"journal-article","created":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T05:34:51Z","timestamp":1637645691000},"page":"936-952","source":"Crossref","is-referenced-by-count":17,"title":["The impact of vaccination on the evolution of COVID-19 in Portugal"],"prefix":"10.3934","volume":"19","author":[{"given":"Beatriz","family":"Machado","sequence":"first","affiliation":[]},{"name":"School of Science and Technology, University of Tr\u00e1s-os-Montes e Alto Douro, UTAD, Quinta de Prados, Vila Real 5001-801, Portugal","sequence":"first","affiliation":[]},{"given":"Liliana","family":"Antunes","sequence":"additional","affiliation":[]},{"given":"Constantino","family":"Caetano","sequence":"additional","affiliation":[]},{"given":"Jo\u00e3o F.","family":"Pereira","sequence":"additional","affiliation":[]},{"given":"Baltazar","family":"Nunes","sequence":"additional","affiliation":[]},{"given":"Paula","family":"Patr\u00edcio","sequence":"additional","affiliation":[]},{"given":"M. Lu\u00edsa","family":"Morgado","sequence":"additional","affiliation":[]},{"name":"Departamento de Epidemiologia, Instituto Nacional de Sa\u00fade Doutor Ricardo Jorge (INSA), Lisbon 1649-016, Portugal","sequence":"additional","affiliation":[]},{"name":"Escola Nacional de Sa\u00fade P\u00fablica, Universidade NOVA de Lisboa","sequence":"additional","affiliation":[]},{"name":"Center for Mathematics and Applications (CMA) and Department of Mathematics, NOVA School of Science and Technology, FCT NOVA, Quinta da Torre, Caparica 2829-516, Portugal","sequence":"additional","affiliation":[]},{"name":"Center for Computational and Stochastic Mathematics, Instituto Superior T\u00e9cnico, University of Lisbon, Lisbon 1049-001, Portugal","sequence":"additional","affiliation":[]}],"member":"2321","reference":[{"key":"key-10.3934\/mbe.2022043-1","doi-asserted-by":"publisher","unstructured":"T. Singhal, A review of coronavirus disease-2019 (COVID-19), <i>Indian J. Pediatr<\/i>, <b>87<\/b> (2020), 281\u2013286. doi: 10.1007\/s12098-020-03263-6.","DOI":"10.1007\/s12098-020-03263-6"},{"key":"key-10.3934\/mbe.2022043-2","doi-asserted-by":"publisher","unstructured":"A. Mavragani, K. Gkillas, Exploring the role of non-pharmaceutical interventions (NPIs) in flattening the Greek COVID-19 epidemic curve, <i>Sci. Rep.<\/i>, <b>11<\/b> (2021), 11741. doi: 10.1038\/s41598-021-90293-5.","DOI":"10.1038\/s41598-021-90293-5"},{"key":"key-10.3934\/mbe.2022043-3","doi-asserted-by":"publisher","unstructured":"C. Pawlowski, P. Lenehan, A. Puranik, V. Agarwal, A. J. Venkatakrishnan, M. J. M. Niesen, et al., FDA-authorized mRNA COVID-19 vaccines are effective per real-world evidence synthesized across a multi-state health system, <i>Med<\/i>, <b>2<\/b> (2021), 979\u2013992. doi: 10.1016\/j.medj.2021.06.007.","DOI":"10.1016\/j.medj.2021.06.007"},{"key":"key-10.3934\/mbe.2022043-4","doi-asserted-by":"publisher","unstructured":"Z. Wang, C. T. Bauch, S. Bhattacharyya, A. d'Onofrio, P. Manfredi, M. Perc, et al., Statistical physics of vaccination, <i>Phys. Rep.<\/i>, <b>664<\/b> (2016), 1\u2013113. doi: 10.1016\/j.physrep.2016.10.006.","DOI":"10.1016\/j.physrep.2016.10.006"},{"key":"key-10.3934\/mbe.2022043-5","doi-asserted-by":"crossref","unstructured":"Z. Memon, S. Qureshi, B. R. Memon, Assessing the role of quarantine and isolation as control strategies for COVID-19 outbreak: a case study, <i>Chaos Solutions Factals<\/i>, <b>144<\/b> (2021). doi: <a href=\"http:\/\/dx.doi.org\/10.1016\/j.chaos.2021.110655\" target=\"_blank\">10.1016\/j.chaos.2021.110655<\/a>.","DOI":"10.1016\/j.chaos.2021.110655"},{"key":"key-10.3934\/mbe.2022043-6","doi-asserted-by":"publisher","unstructured":"S. S. Musa, S. Qureshi, S. Zhao, A. Yusuf, U. T. Mustapha, D. He, Mathematical modeling of COVID-19 epidemic with effect of awareness programs, <i>Infect. Dis. Model.<\/i>, <b>6<\/b> (2021), 448-460. doi: 10.1016\/j.idm.2021.01.012.","DOI":"10.1016\/j.idm.2021.01.012"},{"key":"key-10.3934\/mbe.2022043-7","doi-asserted-by":"crossref","unstructured":"O. J. Peter, S. Qureshi, A. Yusuf, M. Al-Shomrani, A. A. Idowu, A new mathematical model of COVID-19 using real data from Pakista, <i>Results Phys.<\/i>, <b>24<\/b> (2021). doi: <a href=\"http:\/\/dx.doi.org\/10.1016\/j.rinp.2021.104098\" target=\"_blank\">10.1016\/j.rinp.2021.104098<\/a>.","DOI":"10.1016\/j.rinp.2021.104098"},{"key":"key-10.3934\/mbe.2022043-8","doi-asserted-by":"crossref","unstructured":"M. Amouch, N. Karim, Modeling the dynamic of COVID-19 with different types of transmissions, <i>Chaos Solitions Fractals<\/i>, <b>150<\/b> (2021). doi: <a href=\"http:\/\/dx.doi.org\/10.1016\/j.chaos.2021.111188\" target=\"_blank\">10.1016\/j.chaos.2021.111188<\/a>.","DOI":"10.1016\/j.chaos.2021.111188"},{"key":"key-10.3934\/mbe.2022043-9","doi-asserted-by":"publisher","unstructured":"P. Harjule, V. Tiwari, A. Kumar, Mathematical models to predict COVID-19 outbreak : an interim review, <i>J. Int. Math.<\/i>, <b>24<\/b> (2021), 259\u2013284. doi: 10.1080\/09720502.2020.1848316.","DOI":"10.1080\/09720502.2020.1848316"},{"key":"key-10.3934\/mbe.2022043-10","doi-asserted-by":"publisher","unstructured":"S. Moore, E. M. Hill, M. J. Tildesley, L. Dyson, M. J. Keeling, Vaccination and non-pharmaceutical interventions for COVID-19: a mathematical modelling study, <i>Lancet Infect. Dis.<\/i>, <b>21<\/b> (2021), 793\u2013802. doi: 10.1016\/S1473-3099(21)00143-2.","DOI":"10.1016\/S1473-3099(21)00143-2"},{"key":"key-10.3934\/mbe.2022043-11","doi-asserted-by":"publisher","unstructured":"C. Caetano, M. L. Morgado, P. Patr\u00edcio, J. F. Pereira, B. Nunes, Mathematical modelling of the impact of non-pharmacological strategies to control the COVID-19 epidemic in Portugal, <i>Mathematics<\/i>, <b>9<\/b> (2021), 1084. doi: 10.3390\/math9101084.","DOI":"10.3390\/math9101084"},{"key":"key-10.3934\/mbe.2022043-12","doi-asserted-by":"publisher","unstructured":"A. P. Lemos-Pai\u00e3o, C. J. Silva, D. F. M. Torres, A new compartmental epidemiological model for COVID-19 with a case study of Portugal, <i>Ecol. Complex.<\/i>, <b>44<\/b> (2020), 100885. doi: 10.1016\/j.ecocom.2020.100885.","DOI":"10.1016\/j.ecocom.2020.100885"},{"key":"key-10.3934\/mbe.2022043-13","doi-asserted-by":"publisher","unstructured":"J. Viana, C. H. van Dorp, A. Nunes, M. C. Gomes, M. van Boven, M. E. Kretzschmar, et al., Controlling the pandemic during the SARS-CoV-2 vaccination rollout, <i>Nat. Commun.<\/i>, <b>12<\/b> (2021), 3674. doi: 10.21203\/rs.3.rs-358417\/v1.","DOI":"10.21203\/rs.3.rs-358417\/v1"},{"key":"key-10.3934\/mbe.2022043-14","doi-asserted-by":"publisher","unstructured":"D. H. Glass, European and US lockdowns and second waves during the COVID-19 pandemic, <i>Math. Biosci.<\/i>, <b>330<\/b> (2020), 108472. doi: 10.1016\/j.mbs.2020.108472.","DOI":"10.1016\/j.mbs.2020.108472"},{"key":"key-10.3934\/mbe.2022043-15","doi-asserted-by":"publisher","unstructured":"K. Markowitz, M. Strickland, A. Huang, Fever and other clinical indicators may fail to detect COVID-19\u2013infected individuals, <i>J. Evidence Based Dental Pract.<\/i>, <b>20<\/b> (2020), 101499. doi: 10.1016\/j.jebdp.2020.101499.","DOI":"10.1016\/j.jebdp.2020.101499"},{"key":"key-10.3934\/mbe.2022043-16","doi-asserted-by":"crossref","unstructured":"W. Andrew, D. McEvoy, A. B. Collins, K. Hunt, M. Casey, A. Barber, et al., Inferred duration of infectious period of SARS-CoV-2: rapid scoping review and analysis of available evidence for asymptomatic and symptomatic COVID-19 cases, <i>BMJ Open<\/i>, <b>10<\/b> (2020). doi: <a href=\"http:\/\/dx.doi.org\/10.1136\/bmjopen-2020-039856\" target=\"_blank\">10.1136\/bmjopen-2020-039856<\/a>.","DOI":"10.1136\/bmjopen-2020-039856"},{"key":"key-10.3934\/mbe.2022043-17","doi-asserted-by":"publisher","unstructured":"N. Barda, N. Dagan, R. D. Balicer, BNT162b2 mRNA COVID-19 vaccine in a nationwide mass vaccination setting, <i>N. Engl. J. Med.<\/i>, <b>384<\/b> (2021), 1412\u20131423. doi: 10.1056\/NEJMoa2101765.","DOI":"10.1056\/NEJMoa2101765"},{"key":"key-10.3934\/mbe.2022043-18","doi-asserted-by":"crossref","unstructured":"P. T. Heath, E. P. Galiza, D. N. Baxter, M. Boffito, D. Browne, F. Burns, et al., Safety and efficacy of NVX-CoV2373 COVID-19 vaccine, <i>N. Engl. J. Med.<\/i>, <b>30<\/b> (2021). doi: <a href=\"http:\/\/dx.doi.org\/10.1056\/NEJMoa2107659\" target=\"_blank\">10.1056\/NEJMoa2107659<\/a>.","DOI":"10.1056\/NEJMoa2107659"}],"container-title":["Mathematical Biosciences and Engineering"],"original-title":[],"link":[{"URL":"http:\/\/www.aimspress.com\/article\/doi\/10.3934\/mbe.2022043?viewType=html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T05:34:54Z","timestamp":1637645694000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.aimspress.com\/article\/doi\/10.3934\/mbe.2022043"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021]]}},"URL":"https:\/\/doi.org\/10.3934\/mbe.2022043","relation":{},"ISSN":["1551-0018"],"issn-type":[{"type":"print","value":"1551-0018"}],"subject":[],"published":{"date-parts":[[2021]]}}}