Stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates (Articolo in rivista)

Type
Label
  • Stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates (Articolo in rivista) (literal)
Anno
  • 2012-01-01T00:00:00+01:00 (literal)
Alternative label
  • Enatsu, Y.; Messina, E.; Muroya, Y.; Nakata; Y., Russo; E., Vecchio, A. (2012)
    Stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates
    in Applied mathematics and computation
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Enatsu, Y.; Messina, E.; Muroya, Y.; Nakata; Y., Russo; E., Vecchio, A. (literal)
Pagina inizio
  • 5327 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 218 (literal)
Rivista
Note
  • Scopus (literal)
  • Google Scholar (literal)
  • athematical Reviews on the web (MathSciNet) (literal)
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Enatsu; Department of Pure and Applied Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan Mwssina,Russo; Dipartimento di Matematica e Applicazioni, Universit Degli Studi di Napoli Federico II, Via Cintia, I-80126 Napoli, Italy Muroya; Department of Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan Nakata; Basque Center for Applied Mathematics, Bizkaia Technology Park, Building 500, E-48160 Derio, Spain Vecchio; Ist. per Appl. Del Calcolo M. Picone, Sede di Napoli, CNR, Via P. Castellino, 111-80131 Napoli, Italy (literal)
Titolo
  • Stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates (literal)
Abstract
  • We analyze stability of equilibria for a delayed SIR epidemic model, in which population growth is subject to logistic growth in absence of disease, with a nonlinear incidence rate satisfying suitable monotonicity conditions. The model admits a unique endemic equilibrium if and only if the basic reproduction number R 0 exceeds one, while the trivial equilibrium and the disease-free equilibrium always exist. First we show that the disease-free equilibrium is globally asymptotically stable if and only if R 0 <= 1. Second we show that the model is permanent if and only if R 0 > 1. Moreover, using a threshold parameter R 0 characterized by the nonlinear incidence function, we establish that the endemic equilibrium is locally asymptotically stable for 1< R0<=R 0 and it loses stability as the length of the delay increases past a critical value for 1
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