{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T03:17:37Z","timestamp":1771989457213,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,2,7]],"date-time":"2021-02-07T00:00:00Z","timestamp":1612656000000},"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 a 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>The novel coronavirus disease (COVID-19) pneumonia has posed a great threat to the world recent months by causing many deaths and enormous economic damage worldwide. The first case of COVID-19 in Morocco was reported on 2 March 2020, and the number of reported cases has increased day by day. In this work, we extend the well-known SIR compartmental model to deterministic and stochastic time-delayed models in order to predict the epidemiological trend of COVID-19 in Morocco and to assess the potential role of multiple preventive measures and strategies imposed by Moroccan authorities. The main features of the work include the well-posedness of the models and conditions under which the COVID-19 may become extinct or persist in the population. Parameter values have been estimated from real data and numerical simulations are presented for forecasting the COVID-19 spreading as well as verification of theoretical results.<\/jats:p>","DOI":"10.3390\/axioms10010018","type":"journal-article","created":{"date-parts":[[2021,2,8]],"date-time":"2021-02-08T20:51:51Z","timestamp":1612817511000},"page":"18","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":39,"title":["Modeling and Forecasting of COVID-19 Spreading by Delayed Stochastic Differential Equations"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4488-2191","authenticated-orcid":false,"given":"Marouane","family":"Mahrouf","sequence":"first","affiliation":[{"name":"Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M\u2019sik, Hassan II University of Casablanca, Sidi Othman, P.B. 7955 Casablanca, Morocco"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5755-2661","authenticated-orcid":false,"given":"Adnane","family":"Boukhouima","sequence":"additional","affiliation":[{"name":"Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M\u2019sik, Hassan II University of Casablanca, Sidi Othman, P.B. 7955 Casablanca, Morocco"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8412-7783","authenticated-orcid":false,"given":"Houssine","family":"Zine","sequence":"additional","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3604-3841","authenticated-orcid":false,"given":"El Mehdi","family":"Lotfi","sequence":"additional","affiliation":[{"name":"Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M\u2019sik, Hassan II University of Casablanca, Sidi Othman, P.B. 7955 Casablanca, Morocco"}]},{"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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8435-5981","authenticated-orcid":false,"given":"Noura","family":"Yousfi","sequence":"additional","affiliation":[{"name":"Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M\u2019sik, Hassan II University of Casablanca, Sidi Othman, P.B. 7955 Casablanca, Morocco"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2050135","DOI":"10.1142\/S0129183120501351","article-title":"Modeling the early evolution of the COVID-19 in Brazil: Results from a susceptible-infectious-quarantined-recovered (SIQR) model, Internat","volume":"31","author":"Crokidakis","year":"2020","journal-title":"J. Mod. Phys. 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Available online: https:\/\/www.worldometers.info\/coronavirus\/#countries."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/1\/18\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:20:53Z","timestamp":1760160053000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/1\/18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,7]]},"references-count":33,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,3]]}},"alternative-id":["axioms10010018"],"URL":"https:\/\/doi.org\/10.3390\/axioms10010018","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,7]]}}}