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. 2001 Dec 13;414(6865):716-23.
doi: 10.1038/414716a.

Travelling waves and spatial hierarchies in measles epidemics

B T Grenfell  1 , O N Bjørnstad, J Kappey
Affiliations

Travelling waves and spatial hierarchies in measles epidemics

B T Grenfell et al. Nature. .

Abstract

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 pre-vaccination 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.

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Comment in

  • Waving goodbye to measles.
    Strebel PM, Cochi SL. Strebel PM, et al. Nature. 2001 Dec 13;414(6865):695-6. doi: 10.1038/414695a. Nature. 2001. PMID: 11742373 No abstract available.

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