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Science 3 August 1990:
Vol. 249. no. 4968, pp. 499 - 504
DOI: 10.1126/science.2382131
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Articles

Science, Vol 249, Issue 4968, 499-504
Copyright © 1990 by American Association for the Advancement of Science

articles

Chaos versus noisy periodicity: alternative hypotheses for childhood epidemics

LF Olsen and WM Schaffer

Department of Biochemistry, Odense University, Denmark.

Whereas case rates for some childhood diseases (chickenpox) often vary according to an almost regular annual cycle, the incidence of more efficiently transmitted infections such as measles is more variable. Three hypotheses have been proposed to account for such fluctuations. (i) Irregular dynamics result from random shocks to systems with stable equilibria. (ii) The intrinsic dynamics correspond to biennial cycles that are subject to stochastic forcing. (iii) Aperiodic fluctuations are intrinsic to the epidemiology. Comparison of real world data and epidemiological models suggests that measles epidemics are inherently chaotic. Conversely, the extent to which chickenpox outbreaks approximate a yearly cycle depends inversely on the population size.


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