Abstract
Whereas childhood infections such as chickenpox evidence effectively periodic dynamics, case reports for diseases such as measles and rubella fluctuate more erratically [1]. Elsewhere [2,3], it has been suggested that the observed fluctuations correspond to low dimensional chaos of the sort which arises in epidemiological models [5] of the SEIR variety, i.e., differential equations, subject to periodic forcing.1 The basis for this assertion is as follows:
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1.
Reconstructed phase portraits, Poincaré sections, and return maps constructed from actual data are remarkably similar to those obtained from the models (Fig. 1).
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2.
For measles, both the models and the data yield correlation dimensions of about 25. A comparable value is obtained for the Lyapunov dimension as computed directly from the differential equations.
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3.
Both the models and the data yield estimated positive Lyapunov exponents of between 0.4 and 0.5 bpy.
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© 1989 Plenum Press, New York
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Schaffer, W.M., Olsen, L.F. (1989). Chaos in Childhood Epidemics. In: Abraham, N.B., Albano, A.M., Passamante, A., Rapp, P.E. (eds) Measures of Complexity and Chaos. NATO ASI Series, vol 208. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0623-9_22
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DOI: https://doi.org/10.1007/978-1-4757-0623-9_22
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