Discrete and Continuum Models of Crime Pattern Formation P. Jeffrey Brantingham and Andrea Bertozzi Summary of Achievements ARO MURI First Annual Review Meeting, November 28, 2007

Summary of Achievements Development of discrete and continuum models of residential burglary based on known behavior of criminal offenders Qualitative comparisons of discrete and continuum models Stability analyses of continuum models and identification of primary burglary regimes Current efforts in application of models to real geographic environments and crime patterns in Los Angeles and Long Beach Tailoring models to consider terrorist/insurgent activities

crime patterns & hotspot policing routine movements of offenders, victims & security generate crime opportunities crime hotspots are persistent & dynamic results of hotspot policing variable need to understand… fundamental dynamics of hotspot formation, persistence & dissipation how hotspots respond to perturbations Residential burglaries in Long Beach, CA June-August, 2001

repeat & near repeat burglary burglary at one location increases likelihood of repeat event in close spatial proximity repeat occurs soon after the first ‘communication’ of burglary risk is a contagion-like process boundedly-rational offenders prefer known nearby targets The communication of burglary risk is expected to be higher in areas of target homogeneity. exact repeat residential burglary in Long Beach, CA

residential burglary in Long Beach, CA Data for this portion of the project were provided by the Long Beach Police Department and include: 12,690 address geocoded burglaries between Jan 1, 2000 – Dec 31, 2005 Address geocoded residence locations for 861 suspects or arrestees associated with one or more burglaries. 3,951 repeat burglaries at same residence location.

discrete model of residential burglary

continuous model

model results discrete continuous time

burglary regimes Spatial homogeneity Transient hotspots attractiveness field same at all points. Any local increases disappear quickly Transient hotspots localized spots form and remain for varying lengths of time Stationary hotspots stationary spots of high attractiveness are surrounded by areas of extremely low attractiveness.

stability analyses & spatial patterns

current work mapping to real environments testing models with real crime data finite size effects & noise potentially very important role for non-linear filtering & change detection? extend models to deal with insurgent/terrorist activities based on the premise that the behavioral & environmental constraints on criminal behavior are fundamentally the same as those that confront other illicit behaviors