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Melnikov analysis of chaos in a general epidemiological model. (English) Zbl 1114.37050
Summary: The purpose of this paper is to study a SIR model of epidemic dynamics with a periodically modulated nonlinear incidence rate. We must go, for the first time, through a series of coordinate transformations to bring the equations into amenable to Melnikov analysis. This analysis establishes mathematically the existence of chaotic motion of the models by Melnikov’s method. The numerical simulations are made for the conclusions in this paper.

MSC:
37N25Dynamical systems in biology
92D30Epidemiology