{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T23:28:48Z","timestamp":1780442928908,"version":"3.54.1"},"reference-count":34,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,4]],"date-time":"2021-08-04T00:00:00Z","timestamp":1628035200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo\u2013Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder\u2019s and Banach\u2019s fixed point theorems.<\/jats:p>","DOI":"10.3390\/sym13081431","type":"journal-article","created":{"date-parts":[[2021,8,4]],"date-time":"2021-08-04T21:44:24Z","timestamp":1628113464000},"page":"1431","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Stability Analysis and Existence of Solutions for a Modified SIRD Model of COVID-19 with Fractional Derivatives"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8216-3812","authenticated-orcid":false,"given":"Bilal","family":"Basti","sequence":"first","affiliation":[{"name":"Department of Mathematics and Informatics, Ziane Achour University of Djelfa, Djelfa 17000, Algeria"},{"name":"Laboratory of Pure and Applied Mathematics, University of Mohamed Boudiaf M\u2019Sila, M\u2019Sila 28000, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8997-663X","authenticated-orcid":false,"given":"Nacereddine","family":"Hammami","sequence":"additional","affiliation":[{"name":"Computer Engineering Department, College of Engineering and Computer Sciences, Mustaqbal University, Buraydah 52547, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8020-7823","authenticated-orcid":false,"given":"Imadeddine","family":"Berrabah","sequence":"additional","affiliation":[{"name":"Laboratory of Pure and Applied Mathematics, University of Mohamed Boudiaf M\u2019Sila, M\u2019Sila 28000, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6505-9797","authenticated-orcid":false,"given":"Farid","family":"Nouioua","sequence":"additional","affiliation":[{"name":"Laboratoire de Math\u00e9matique et Physique Appliqu\u00e9es, \u00c9cole Normale Sup\u00e9rieure de Bousaada, Bousaada 28001, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rabah","family":"Djemiat","sequence":"additional","affiliation":[{"name":"Laboratory of Pure and Applied Mathematics, University of Mohamed Boudiaf M\u2019Sila, M\u2019Sila 28000, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5740-8504","authenticated-orcid":false,"given":"Noureddine","family":"Benhamidouche","sequence":"additional","affiliation":[{"name":"Laboratory of Pure and Applied Mathematics, University of Mohamed Boudiaf M\u2019Sila, M\u2019Sila 28000, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,4]]},"reference":[{"key":"ref_1","unstructured":"(The New York Times, 2020). 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