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2011, Volume 2011: 1119-1128. Doi: 10.3934/proc.2011.2011.1119 open access
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On the global stability of an SIRS epidemic model with distributed delays

  • 1.

    Basque Center for Applied Mathematics, Bizkaia Technology Park, Building 500 E-48160 Derio

  • 2.

    Department of Pure and Applied Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555

  • 3.

    Department of Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555

Received:  June 30, 2010
Revised:  July 31, 2010
Published:  August 2017
Abstract Related Papers Cited by
    Abstract
  • In this paper, we establish the global asymptotic stability of an endemic equilibrium for an SIRS epidemic model with distributed time delays. It is shown that the global stability holds for any rate of immunity loss, if the basic reproduction number is greater than 1 and less than or equals to a critical value. Otherwise, there is a maximal rate of immunity loss which guarantees the global stability. By using an extension of a Lyapunov functional established by [C.C. McCluskey, Complete global stability for an SIR epidemic model with delay-Distributed or discrete, Nonlinear Anal. RWA. 11 (2010) 55-59], we provide a partial answer to an open problem whether the endemic equilibrium is globally stable, whenever it exists, or not.
    Mathematics Subject Classification: Primary: 34K20 and 34K25; Secondary: 92D30.

    Citation:
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