Low Dimensional Strange Attractors in Epidemics of Childhood Diseases in Copenhagen, Denmark
The monthly reported cases of six childhood diseases in Copenhagen, Denmark over periods of 30–40 years were analysed by three different non-linear techniques: (1) Calculation of the correlation dimension, (2) calculation of the Lyapunov exponents from apparently 1D maps derived from Poincaré sections of the flows and (3) calculation of the maximal Lyapunov exponents from the flows. Combining the results from these three types of analysis leads to the following conclusions: three of the diseases (measles, mumps and rubella) evolve with chaotic dynamics, one disease (chicken pox) evolves with dynamics corresponding to a noise-perturbed damped oscillation and the remaining two diseases (pertussis and scarlet fever) evolve with dynamics that are completely obscured by random fluctuations.
KeywordsLyapunov Exponent Chaotic Dynamic Chaotic Attractor Reporting Rate Childhood Disease
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