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, 35 (3), 359-73

Melnikov Analysis of Chaos in a Simple Epidemiological Model

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Melnikov Analysis of Chaos in a Simple Epidemiological Model

P Glendinning et al. J Math Biol.

Abstract

Melnikov's method is applied to an SIR model of epidemic dynamics with a periodically modulated nonlinear incidence rate. This analysis establishes mathematically, for the first time, the existence of chaotic motion in these models. A related technique also makes it possible to prove that homoclinic bifurcations occurs in the model.

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