Chayes. Statistical models of criminal behavior: The effects of law enforcement actions

We extend an agent-based model of crime-pattern formation initiated in Short et al. by incor-porating the e®ects of law enforcement agents. We investigate the e®ect that these agents have on the spatial distribution and overall level of criminal activity in a simulated urban setting. Our focus is on a two-dimensional lattice model of residential burglaries, where each site (target) is characterized by a dynamic attractiveness to burglary and where criminal and law enforcement agents are represented by random walkers. The dynamics of the criminal agents and the target-attractiveness ¯eld are, with certain modi¯cations, as described in Short et al. Here the dynamics of enforcement agents are a®ected by the attractiveness ¯eld via a biasing of the walk, the detailed rules of which de¯ne a deployment strategy. We observe that law enforcement agents, if properly deployed, will in fact reduce the total amount of crime, but their relative e®ectiveness depends on the number of agents deployed, the deployment strategy used, and spatial distri-bution of criminal activity. For certain policing strategies, continuum PDE models can be derived from the discrete systems. The continuum models are qualitatively similar to the discrete systems at large system sizes