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Melnikov analysis of chaos in a simple epidemiological model
1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK. P.A.Glendinning@qmw.ac.uk, 1pp@runge.ampt.cam.ac.uk
Journal of Mathematical Biology
|February 1, 1997
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.