On the global stability of an SIRS epidemic model with distributed delays | Zendy

Yukihiko Nakata | Zendy; Yoichi Enatsu | Zendy; Yoshiaki Muroya | Zendy

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On the global stability of an SIRS epidemic model with distributed delays

Author(s) -

Yukihiko Nakata,

Yoichi Enatsu,

Yoshiaki Muroya

Publication year - 2011

Publication title -

conference publications

Language(s) - English

Resource type - Book series

DOI - 10.3934/proc.2011.2011.1119

Subject(s) - epidemic model , stability (learning theory) , basic reproduction number , exponential stability , mathematics , lyapunov function , extension (predicate logic) , nonlinear system , mathematical economics , control theory (sociology) , computer science , demography , physics , artificial intelligence , population , sociology , control (management) , quantum mechanics , machine learning , programming language

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.

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