Stochastic dynamics and a power law for measles variability

Matt Keeling, Bryan Grenfell

Research output: Contribution to journalArticlepeer-review

68 Scopus citations


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
Issue number1384
StatePublished - Apr 29 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Biochemistry, Genetics and Molecular Biology
  • General Agricultural and Biological Sciences


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


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