Filling the gaps: A robust description of adhesive birth-death-movement processes

Existing continuum descriptions of discrete adhesive birth-death-movement processes provide accurate predictions of the average discrete behavior for limited parameter regimes. Here we present an alternative continuum description in terms of the dynamics of groups of contiguous occupied and vacant lattice sites. Our method provides more accurate predictions, is valid in parameter regimes that could not be described by previous continuum descriptions, and provides information about the spatial clustering of occupied sites. Furthermore, we present a simple analytic approximation of the spatial clustering of occupied sites at late time, when the system reaches its steady-state configuration.