Stochastic dynamics and a power law for measles variability

Matt Keeling, Bryan Grenfell

Research output: Contribution to journalArticlepeer-review

57 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)769-776
Number of pages8
JournalPhilosophical Transactions of the Royal Society B: Biological Sciences
Volume354
Issue number1384
DOIs
StatePublished - Apr 29 1999

All Science Journal Classification (ASJC) codes

  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)

Keywords

  • Critical community size
  • Measles
  • Power law
  • Stochasticity
  • Vaccination

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