Spatial structure and fluctuations in the contact process and related models

The contact process is used as a simple spatial model in many disciplines, yet because of the buildup of spatial correlations, its dynamics remain dif ficult to capture analytically. We introduce an empirically based, approxim ate method of characterizing the spatial correlations with only a single ad justable parameter. This approximation allows us to recast the contact proc ess in terms of a stochastic birth-death process, converting a spatiotempor al problem into a simpler temporal one. We obtain considerably more accurat e predictions of equilibrium population than those given by pair approximat ions, as well as good predictions of population variance and first passage time distributions to a given (low) threshold. A similar approach is applic able to any model with a combination of global and nearest-neighbor interac tions. (C) 2000 Society for Mathematical Biology.