Measles metapopulation dynamics: A gravity model for epidemiological coupling and dynamics

Yingcun Xia, Ottar N. Bjørnstad, Bryan T. Grenfell

Research output: Contribution to journalArticlepeer-review

243 Scopus citations


Infectious diseases provide a particularly clear illustration of the spatiotemporal underpinnings of consumer-resource dynamics. The paradigm is provided by extremely contagious, acute, immunizing childhood infections. Partially synchronized, unstable oscillations are punctuated by local extinctions. This, in turn, can result in spatial differentiation in the timing of epidemics and, depending on the nature of spatial contagion, may result in traveling waves. Measles epidemics are one of a few systems documented well enough to reveal all of these properties and how they are affected by spatiotemporal variations in population structure and demography. On the basis of a gravity coupling model and a time series susceptible-infected-recovered (TSIR) model for local dynamics, we propose a metapopulation model for regional measles dynamics. The model can capture all the major spatiotemporal properties in prevaccination epidemics of measles in England and Wales.

Original languageEnglish (US)
Pages (from-to)267-281
Number of pages15
JournalAmerican Naturalist
Issue number2
StatePublished - Aug 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Ecology, Evolution, Behavior and Systematics


  • Gravity models
  • Measles
  • Phase difference
  • SIR model
  • TSIR model
  • Wavelet


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