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Title: Global stability condition for the disease-free equilibrium point of fractional epidemiological models
Author: Almeida, Ricardo
Martins, Natália
Silva, Cristiana J.
Keywords: Epidemiology
Mathematical modeling
Fractional calculus
Issue Date: 2021
Publisher: MDPI
Abstract: 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–Leffler 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.
Peer review: yes
DOI: 10.3390/axioms10040238
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Appears in Collections:CIDMA - Artigos
DMat - Artigos
SCG - Artigos

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