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J Math Biol. 1997 Feb;35(3):359-73.

Melnikov analysis of chaos in a simple epidemiological model.

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1
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK. P.A.Glendinning@qmw.ac.uk, 1pp@runge.ampt.cam.ac.uk

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.

PMID:
9120378
[Indexed for MEDLINE]
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