{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T21:55:28Z","timestamp":1771710928166,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,9,25]],"date-time":"2021-09-25T00:00:00Z","timestamp":1632528000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we present a new result that allows for studying the global stability of the disease-free equilibrium point when the basic reproduction number is less than 1, in the fractional calculus context. The method only involves basic linear algebra and can be easily applied to study global asymptotic stability. After proving some auxiliary lemmas involving the Mittag\u2013Leffler function, we present the main result of the paper. Under some assumptions, we prove that the disease-free equilibrium point of a fractional differential system is globally asymptotically stable. We then exemplify the procedure with some epidemiological models: a fractional-order SEIR model with classical incidence function, a fractional-order SIRS model with a general incidence function, and a fractional-order model for HIV\/AIDS.<\/jats:p>","DOI":"10.3390\/axioms10040238","type":"journal-article","created":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T01:59:47Z","timestamp":1632707987000},"page":"238","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Global Stability Condition for the Disease-Free Equilibrium Point of Fractional Epidemiological Models"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1305-2411","authenticated-orcid":false,"given":"Ricardo","family":"Almeida","sequence":"first","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\/0000-0003-3535-3909","authenticated-orcid":false,"given":"Nat\u00e1lia","family":"Martins","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\/0000-0002-7238-546X","authenticated-orcid":false,"given":"Cristiana J.","family":"Silva","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":[[2021,9,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.cnsns.2017.04.001","article-title":"The role of fractional calculus in modeling biological phenomena: A review","volume":"51","author":"Ionescu","year":"2017","journal-title":"Commun. 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