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Zbl 1114.37050
Diallo, Ouaténi; Koné, Yaya
Melnikov analysis of chaos in a general epidemiological model. (English)
[J] Nonlinear Anal., Real World Appl. 8, No. 1, 20-26 (2007). ISSN 1468-1218

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 2000:: *37N25 Dynamical systems in biology
92D30 Epidemiology

Keywords: infective models; chaos; Melnikov's method; homoclinic orbit

Cited in: Zbl 1238.37039

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