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Science 28 January 2000:
Vol. 287. no. 5453, pp. 667 - 670
DOI: 10.1126/science.287.5453.667
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Reports

A Simple Model for Complex Dynamical Transitions in Epidemics

David J. D. Earn, 12* Pejman Rohani, 2 Benjamin M. Bolker, 3 Bryan T. Grenfell 2

Dramatic changes in patterns of epidemics have been observed throughout this century. For childhood infectious diseases such as measles, the major transitions are between regular cycles and irregular, possibly chaotic epidemics, and from regionally synchronized oscillations to complex, spatially incoherent epidemics. A simple model can explain both kinds of transitions as the consequences of changes in birth and vaccination rates. Measles is a natural ecological system that exhibits different dynamical transitions at different times and places, yet all of these transitions can be predicted as bifurcations of a single nonlinear model.

1 Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada.
2 Department of Zoology, University of Cambridge, Downing Street, Cambridge CB2 3EJ, UK.
3 Zoology Department, University of Florida, Gainesville, FL 32611-8525, USA.
*   To whom correspondence should be addressed. E-mail: earn{at}math.mcmaster.ca

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