{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T12:41:04Z","timestamp":1774528864997,"version":"3.50.1"},"reference-count":21,"publisher":"EDP Sciences","license":[{"start":{"date-parts":[[2020,11,11]],"date-time":"2020-11-11T00:00:00Z","timestamp":1605052800000},"content-version":"vor","delay-in-days":315,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Foundation for Science and Technology Portugal - FCT","award":["UIDB\/04106\/2020 (CIDMA)"],"award-info":[{"award-number":["UIDB\/04106\/2020 (CIDMA)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Model. Nat. Phenom."],"accepted":{"date-parts":[[2020,10,28]]},"published-print":{"date-parts":[[2020]]},"abstract":"<jats:p>Coronavirus disease 2019 (COVID-19) poses a great threat to public health and the economy worldwide. Currently, COVID-19 evolves in many countries to a second stage, characterized by the need for the liberation of the economy and relaxation of the human psychological effects. To this end, numerous countries decided to implement adequate deconfinement strategies. After the first prolongation of the established confinement, Morocco moves to the deconfinement stage on May 20, 2020. The relevant question concerns the impact on the COVID-19 propagation by considering an additional degree of realism related to stochastic noises due to the effectiveness level of the adapted measures. In this paper, we propose a delayed stochastic mathematical model to predict the epidemiological trend of COVID-19 in Morocco after the deconfinement. To ensure the well-posedness of the model, we prove the existence and uniqueness of a positive solution. Based on the large number theorem for martingales, we discuss the extinction of the disease under an appropriate threshold parameter. Moreover, numerical simulations are performed in order to test the efficiency of the deconfinement strategies chosen by the Moroccan authorities to help the policy makers and public health administration to make suitable decisions in the near future.<\/jats:p>","DOI":"10.1051\/mmnp\/2020040","type":"journal-article","created":{"date-parts":[[2020,10,28]],"date-time":"2020-10-28T19:59:18Z","timestamp":1603915158000},"page":"50","source":"Crossref","is-referenced-by-count":20,"title":["A stochastic time-delayed model for the effectiveness of Moroccan COVID-19 deconfinement strategy"],"prefix":"10.1051","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8412-7783","authenticated-orcid":false,"given":"Houssine","family":"Zine","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5755-2661","authenticated-orcid":false,"given":"Adnane","family":"Boukhouima","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3604-3841","authenticated-orcid":false,"given":"El Mehdi","family":"Lotfi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4488-2191","authenticated-orcid":false,"given":"Marouane","family":"Mahrouf","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8641-2505","authenticated-orcid":false,"given":"Delfim F.M.","family":"Torres","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8435-5981","authenticated-orcid":false,"given":"Noura","family":"Yousfi","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2020,11,11]]},"reference":[{"key":"R1","unstructured":"Baum S.G., \nCOVID-19 incubation period: An update, Journal Watch. \nAvailable from https:\/\/www.jwatch.org\/na51083\/2020\/03\/13\/covid-19incubation-period-update\n(2020)."},{"key":"R2","doi-asserted-by":"crossref","unstructured":"Boudrioua M.S. and \nBoudrioua A., \nPredicting the COVID-19 epidemic in Algeria using the SIR model. Preprint medRxiv 20079467v1 (2020).","DOI":"10.1101\/2020.04.25.20079467"},{"key":"R3","doi-asserted-by":"crossref","first-page":"109761","DOI":"10.1016\/j.chaos.2020.109761","volume":"134","author":"Fanelli","year":"2020","journal-title":"Chaos Solitons Fract"},{"key":"R4","unstructured":"Gorbalenya A.E., \nBaker S.C., \nBaric R.S., \nde Groot R.J., \nDrosten C., \nGulyaeva A.A., \nHaagmans B.L., \nLauber C., \nLeontovich A.M., \nNeuman B.W., \nPenzar D., \nPerlman S., \nPoon L.L.M., \nSamborskiy D.V., \nSidorov I.A., \nSola I. and \nZiebuhr J., \nThe species severe acute respiratory syndrome related coronavirus: classifying 2019-nCoV and naming it SARS-CoV-2. \nNat. Microbiol. \n(2020) 1\u20139."},{"key":"R5","doi-asserted-by":"crossref","first-page":"876","DOI":"10.1137\/10081856X","volume":"71","author":"Grai","year":"2011","journal-title":"SIAM J. Appl. Math"},{"key":"R6","unstructured":"Haut Conseil de la Sant\u00e9 Publique, \nAvis relatif aux recommandations th\u00e9rapeutiques dans la prise en charge du COVID-19 (compl\u00e9mentaire A l\u2019avis du 5mars 2020). Available from: https:\/\/sfar.org\/avis-relatif-aux-recommandations-therapeutiques-dans-la-prise-en-charge-du-covid-19\/ (2020)."},{"key":"R7","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1137\/S0036144500378302","volume":"43","author":"Higham","year":"2001","journal-title":"SIAM Rev"},{"key":"R8","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/S0140-6736(20)30183-5","volume":"395","author":"Huang","year":"2020","journal-title":"Lancet"},{"key":"R9","doi-asserted-by":"crossref","first-page":"105303","DOI":"10.1016\/j.cnsns.2020.105303","volume":"88","author":"Ivorra","year":"2020","journal-title":"Commun. Nonlinear Sci. Numer. 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Available from: http:\/\/www.covidmaroc.ma\/pages\/Accueil.aspx \n(2020)."},{"key":"R15","doi-asserted-by":"crossref","first-page":"2000180","DOI":"10.2807\/1560-7917.ES.2020.25.10.2000180","volume":"25","author":"Mizumoto","year":"2020","journal-title":"Euro Surveill"},{"key":"R16","doi-asserted-by":"crossref","first-page":"109846","DOI":"10.1016\/j.chaos.2020.109846","volume":"135","author":"Nda\u00efrou","year":"2020","journal-title":"Chaos Solitons Fract"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"Ozair M., \nHussain T., \nHussain M., \nAwan A.U. and \nBaleanu D., \nEstimation of transmission potential and severity of COVID-19 in Romania and Pakistan. \nPreprint medRxiv 20088989v1 (2020).","DOI":"10.1101\/2020.05.02.20088989"},{"key":"R18","doi-asserted-by":"crossref","first-page":"462","DOI":"10.3390\/jcm9020462","volume":"9","author":"Tang","year":"2020","journal-title":"J. Clin. 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Available from: https:\/\/apps.who.int\/iris\/handle\/10665\/331686 (2020)."},{"key":"R21","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1016\/S0140-6736(20)30260-9","volume":"395","author":"Wu","year":"2020","journal-title":"The Lancet"}],"container-title":["Mathematical Modelling of Natural Phenomena"],"original-title":[],"link":[{"URL":"https:\/\/www.mmnp-journal.org\/10.1051\/mmnp\/2020040\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,11]],"date-time":"2020-11-11T20:08:51Z","timestamp":1605125331000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mmnp-journal.org\/10.1051\/mmnp\/2020040"}},"subtitle":[],"editor":[{"given":"E.","family":"Augeraud","sequence":"first","affiliation":[]},{"given":"M.","family":"Banerjee","sequence":"additional","affiliation":[]},{"given":"J.-S.","family":"Dhersin","sequence":"additional","affiliation":[]},{"given":"A.","family":"d'Onofrio","sequence":"additional","affiliation":[]},{"given":"T.","family":"Lipniacki","sequence":"additional","affiliation":[]},{"given":"S.","family":"Petrovskii","sequence":"additional","affiliation":[]},{"given":"Chi","family":"Tran","sequence":"additional","affiliation":[]},{"given":"A.","family":"Veber-Delattre","sequence":"additional","affiliation":[]},{"given":"E.","family":"Vergu","sequence":"additional","affiliation":[]},{"given":"V.","family":"Volpert","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2020]]},"references-count":21,"alternative-id":["mmnp200164"],"URL":"https:\/\/doi.org\/10.1051\/mmnp\/2020040","relation":{},"ISSN":["0973-5348","1760-6101"],"issn-type":[{"value":"0973-5348","type":"print"},{"value":"1760-6101","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020]]}}}