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Global stability of an SIR epidemic model with information dependent vaccination. (English) Zbl 1152.92019
Summary: We study the global behavior of a nonlinear susceptible-infectious-removed (SIR)-like epidemic model with a non-bilinear feedback mechanism, which describes the influence of information, and of information-related delays, on a vaccination campaign. We upgrade the stability analysis performed by A. d’Onofrio, P. Manfredi and E. Salinelli [Vaccinating behavior, information, and the dynamics of SIR vaccine preventable diseases. Theor. Popul. Biol. 71, No. 3, 301–317 (2007; Zbl 1124.92029)] and give a special example of the application of the geometric method for global stability, due to M. Y. Li and J. S. Muldowney [SIAM J. Math. Anal. 27, No. 4, 1070-1083 (1996; Zbl 0873.34041)]. Numerical investigations are provided to show how the stability properties depend on the interplay between some relevant parameters of the model.
MSC:
92D30Epidemiology
34D23Global stability of ODE
65C20Models (numerical methods)
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