title: Melnikov analysis of chaos in a simple epidemiological model.
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.
authors.affiliation: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK. P.A.Glendinning@qmw.ac.uk, 1pp@runge.ampt.cam.ac.uk
authors.forename: P
authors.initials: P
authors.lastname: Glendinning
authors.forename: L P
authors.initials: LP
authors.lastname: Perry
mesh_terms: D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D017711:Nonlinear Dynamics