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POPULATION BIOLOGY
Using conservation of pattern to estimate spatial parameters from a single snapshot

Matt J. Keeling ^*, , Stephen P. Brooks , and Christopher A. Gilligan 

^*Mathematics Institute and Department of Biological Sciences, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom; Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, United Kingdom; and Department of Plant Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EA, United Kingdom

Edited by Burton H. Singer, Princeton University, Princeton, NJ, and approved April 29, 2004 (received for review January 15, 2004)

Rapid reaction in the face of an epidemic is a key element in effective and efficient control; this is especially important when the disease has severe public health or economic consequences. Determining an appropriate level of response requires rapid estimation of the rate of spread of infection from limited disease distribution data. Generally, the techniques used to estimate such spatial parameters require detailed spatial data at multiple time points; such data are often time-consuming and expensive to collect. Here we present an alternative approach that is computationally efficient and only requires spatial data from a single time point, hence saving valuable time at the start of the epidemic. By assuming that fundamental spatial statistics are near equilibrium, parameters can be estimated by minimizing the expected rate of change of these statistics, hence conserving the general spatial pattern. Although applicable to both ecological and epidemiological data, here we focus on disease data from computer simulations and real epidemics to show that this method produces reliable results that could be used in practical situations.

epidemic | spatial spread | parameter estimation | foot-and-mouth disease | citrus tristeza virus

Abbreviation: MCMC, Markov Chain Monte Carlo.

To whom correspondence should be addressed. E-mail: m.j.keeling{at}warwick.ac.uk.

© 2004 by The National Academy of Sciences of the USA

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