Travelling waves and spatial hierarchies in measles epidemics

B. T. Grenfell, O. N. Bjørnstad, J. Kappey

Research output: Contribution to journalArticlepeer-review

717 Scopus citations


Spatio-temporal travelling waves are striking manifestations of predator-prey and host-parasite dynamics. However, few systems are well enough documented both to detect repeated waves and to explain their interaction with spatio-temporal variations in population structure and demography. Here, we demonstrate recurrent epidemic travelling waves in an exhaustive spatio-temporal data set for measles in England and Wales. We use wavelet phase analysis, which allows for dynamical non-stationarity - a complication in interpreting spatio-temporal patterns in these and many other ecological time series. In the prevaccination era, conspicuous hierarchical waves of infection moved regionally from large cities to small towns; the introduction of measles vaccination restricted but did not eliminate this hierarchical contagion. A mechanistic stochastic model suggests a dynamical explanation for the waves - spread via infective 'sparks' from large 'core' cities to smaller 'satellite' towns. Thus, the spatial hierarchy of host population structure is a prerequisite for these infection waves.

Original languageEnglish (US)
Pages (from-to)716-723
Number of pages8
Issue number6865
StatePublished - Dec 13 2001
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General


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