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Philosophical Transactions of the Royal Society B: Biological Sciences logoLink to Philosophical Transactions of the Royal Society B: Biological Sciences
. 1999 Apr 29;354(1384):769–776. doi: 10.1098/rstb.1999.0429

Stochastic dynamics and a power law for measles variability.

M Keeling 1, B Grenfell 1
PMCID: PMC1692561  PMID: 10365402

Abstract

Since the discovery of a power law scaling between the mean and variance of natural populations, this phenomenon has been observed for a variety of species. Here, we show that the same form of power law scaling also occurs in measles case reports in England and Wales. Remarkably this power law holds over four orders of magnitude. We consider how the natural experiment of vaccination affects the slope of the power law. By examining simple generic models, we are able to predict the effects of stochasticity and coupling and we propose a new phenomenon associated with the critical community size.

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Selected References

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