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Global stability of a delayed SIRS epidemic model with a non-monotonic incidence rate |
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| Authors: | Yoshiaki Muroya Yoichi Enatsu |
| Affiliation: | a Department of Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555, Japan b Department of Pure and Applied Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, 169-8555, Japan c Basque Center for Applied Mathematics, Bizkaia Technology Park, Building 500, E-48160, Derio, Spain |
| Abstract: | In this paper, we investigate a disease transmission model of SIRS type with latent period τ?0 and the specific nonmonotone incidence rate, namely,  . For the basic reproduction number R0>1, applying monotone iterative techniques, we establish sufficient conditions for the global asymptotic stability of endemic equilibrium of system which become partial answers to the open problem in [Hai-Feng Huo, Zhan-Ping Ma, Dynamics of a delayed epidemic model with non-monotonic incidence rate, Commun. Nonlinear Sci. Numer. Simul. 15 (2010) 459-468]. Moreover, combining both monotone iterative techniques and the Lyapunov functional techniques to an SIR model by perturbation, we derive another type of sufficient conditions for the global asymptotic stability of the endemic equilibrium. |
| Keywords: | SIRS epidemic model Nonlinear incidence rate Global asymptotic stability Permanence Monotone iterative technique Lyapunov functional technique |
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