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Global stability of a delayed SIRS epidemic model with a non-monotonic incidence rate. (English) Zbl 1242.92053

SIRS epidemic models with latent periods and specific non-monotone incidence rates are investigated. By applying monotone iterative techniques, the authors establish sufficient conditions for the global asymptotic stability of the endemic equilibrium of the system which gives a partial answer to an open problem of H.-F. Huo and Z.-P. Ma [Dynamics of a delayed epidemic model with non-monotonic incidence rate. Commun. Nonlinear Sci. Numer. Simul. 15, No. 2, 459–468 (2010; Zbl 1221.34197)]. Moreover, combining both monotone iterative techniques and Lyapunov functional techniques for the SIRS model by perturbations, they derive another type of sufficient conditions for the global asymptotic stability of the endemic equilibrium.

MSC:

92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
34D05 Asymptotic properties of solutions to ordinary differential equations

Citations:

Zbl 1221.34197
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References:

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