PARENT SESSION
Session #11: The role of parasites and infectious diseases in ecology. Organized by: A. Dobson, L. Real, R. Ostfeld, and R. Holt.
Tuesday, August 7, 2001. Madison Ballroom A
Epidemic waves in the dynamics of measles: wavelets and spatial hierarchies.
Grenfell, Bryan1, Bjornstad, Ottar2, 1 2
ABSTRACT- A basic question for ecological theory is the interaction between spatial population interactions and temporal dynamics, via their impact on spatial pattern formation. For predator-prey and parasite-host systems, theory suggests that 'traveling waves' in abundance or incidence are the most striking outcome of spatio-temporal interactions. However, although complicated space-time patterns are theoretically predicted across a wide variety of systems, supporting empirical evidence is less than overwhelming. Here, we investigate an exhaustive spatio-temporal data set for measles in the cities and villages of England and Wales. We identify two issues of general importance. First, dynamical non-stationarities - ubiquitous in ecological systems - must be allowed for in the search for waves. We solve this problem with a novel application of wavelet phase analysis, revealing dramatic hierarchical waves of measles infection, moving regionally from large cities to small towns at a rate of around 5 km/wk. Second, standard deterministic models fail to explain these hierarchical waves. We develop a fully stochastic model (the coupled TSIR model) that suggests a novel dynamical explanation for the waves - a stochastic spread of infective 'sparks' from large/endemic cities to small/epidemic centers. Our study provides a statistically sound and theoretically consistent demonstration of 'forest fire' dynamics in an endemic epidemiological context.
KEY WORDS: epidemic waves, wavelets, spatial hierarchies, measles