{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T03:12:13Z","timestamp":1768619533565,"version":"3.49.0"},"reference-count":18,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T00:00:00Z","timestamp":1637625600000},"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\/00212\/2020 (CMA-UBI)"],"award-info":[{"award-number":["UIDB\/00212\/2020 (CMA-UBI)"]}],"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 (CIDMA)"],"award-info":[{"award-number":["UIDB\/04106\/2020 (CIDMA)"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Recently, a continuous-time compartmental mathematical model for the spread of the Coronavirus disease 2019 (COVID-19) was presented with Portugal as case study, from 2 March to 4 May 2020, and the local stability of the Disease Free Equilibrium (DFE) was analysed. Here, we propose an analogous discrete-time model and, using a suitable Lyapunov function, we prove the global stability of the DFE point. Using COVID-19 real data, we show, through numerical simulations, the consistence of the obtained theoretical results.<\/jats:p>","DOI":"10.3390\/axioms10040314","type":"journal-article","created":{"date-parts":[[2021,11,24]],"date-time":"2021-11-24T02:46:08Z","timestamp":1637721968000},"page":"314","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Discrete-Time Compartmental Epidemiological Model for COVID-19 with a Case Study for Portugal"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1507-2272","authenticated-orcid":false,"given":"Sandra","family":"Vaz","sequence":"first","affiliation":[{"name":"Center of Mathematics and Applications (CMA-UBI), Department of Mathematics, University of 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":[[2021,11,23]]},"reference":[{"key":"ref_1","unstructured":"(2021, September 16). DGS, COVID-19. Available online: http:\/\/www.covid19.min-saude.pt."},{"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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App. Sci."},{"key":"ref_12","unstructured":"(2021, September 16). DGS, Ponto de Situa\u00e7\u00e3o Atual em Portugal. Available online: https:\/\/covid19.min-saude.pt\/ponto-desitua\u00e7\u00e3oatual-em-portugal."},{"key":"ref_13","unstructured":"(2021, September 16). Pordata. Available online: https:\/\/www.pordata.pt\/Portugal."},{"key":"ref_14","unstructured":"(2021, September 16). Rep\u00fablica Portuguesa, Available online: https:\/\/www.portugal.gov.pt\/download-ficheiros\/ficheiro.aspx?v=b8560501-45e9-4421-b20a-927b6d65e964."},{"key":"ref_15","unstructured":"(2021, September 16). WHO. Available online: https:\/\/www.who.int\/news-room\/q-a-detail\/q-a-coronaviroses."},{"key":"ref_16","unstructured":"(2021, September 16). Neg\u00f3cios, O que Fazem os Portugueses na Quarentena? 40% em Teletrabalho, 10% Fora de Casa. Available online: https:\/\/www.jornaldenegocios.pt\/economia\/coronavirus\/detalhe\/o-que-fazem-os-portugueses-na-quarentena-40-em-teletrabalho-10-fora-de-casa."},{"key":"ref_17","unstructured":"(2021, September 16). RTP. Available online: https:\/\/www.rtp.pt\/noticias\/pa\u00eds\/covid-19-apenas-89-dos-785-infetados-em-portugal-est\u00e3o-intrnados-em-hospitais-v1213491."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Couras, J., Area, I., Nieto, J.J., Silva, C.J., and Torres, D.F.M. (2021). Optimal control of vaccination and plasma transfusion with potential usefulness for COVID-19. 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