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Global dynamics of a delayed SIRS epidemic model with a wide class of nonlinear incidence rates |
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| Authors: | Yoichi Enatsu Eleonora Messina Yukihiko Nakata Yoshiaki Muroya Elvira Russo Antonia Vecchio |
| Institution: | 1. Department of Pure and Applied Mathematics, Waseda University, Ohkubo 3-4-1, Shinjuku-ku, Tokyo, 169-8555, Japan 2. Dipartimento di Matematica e Applicazioni, Universit?? degli Studi di Napoli ??Federico II??, Via Cintia, 80126, Napoli, Italy 3. Basque Center for Applied Mathematics, Bizkaia Technology Park, Building 500, 48160, Derio, Spain 4. Department of Mathematics, Waseda University, Ohkubo 3-4-1, Shinjuku-ku, Tokyo, 169-8555, Japan 5. Ist. per Appl. del Calcolo ??M. Picone?? Sede di Napoli-CNR, Via P. Castellino, 111-80131, Napoli, Italy |
| Abstract: | In this paper, by constructing Lyapunov functionals, we consider the global dynamics of an SIRS epidemic model with a wide class of nonlinear incidence rates and distributed delays $\int^{h}_{0} p(\tau)f(S(t),I(t-\tau)) \mathrm{d}\tau$ under the condition that the total population converges to 1. By using a technical lemma which is derived from strong condition of strict monotonicity of functions f(S,I) and f(S,I)/I with respect to S??0 and I>0, we extend the global stability result for an SIR epidemic model if R 0>1, where R 0 is the basic reproduction number. By using a limit system of the model, we also show that the disease-free equilibrium is globally asymptotically stable if R 0=1. |
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