DHB: Mathematical and Simulation Modeling of Crime Hot Spots

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This project will concentrate on the development of analytical and computational models of crime hot spot formation, persistence and dissipation. Crime hot spots are geographical areas with clusters of criminal offenses occurring within a specified interval of time. Hot spots may consist of clusters of property crimes such as burglaries or auto thefts, or violent crimes such as homicides, which occur on time scales ranging from hours to months. Mapping of crime hot spots is important in current approaches to understanding criminal offender behavior and is a tool used increasingly by police departments and policy makers for strategic crime prevention. However, despite the availability of sophisticated digital mapping and analysis tools there is a substantial gap in the understanding of how low-level behaviors of offenders lead to aggregate crime patterns including crime hot spots. Thus, for example, it is not possible to specify exactly why directed police action at crime hot spots sometimes leads to displacement of crime in space but, surprisingly, often can also lead to hot spot dissipation and a real reduction in crime incidences. Drawing on analytical methods in statistical physics, the mathematics of swarms, and new techniques in agent-based computational modeling, formal models of offender movement and target selection will be developed and simulated in different environments. These baseline models will be extended to consider offender behavior on abstract urban street networks and then integrate both model types with Geographic Information Systems (GIS) by exploring the spatial properties of simulated crime maps. Finally, at each stage of model development, empirical tests will be conducted against spatial crime data provided by the Los Angeles, San Diego and Long Beach Police Departments. The project will help clarify the quantitative relationships between criminal behavior, criminal opportunities and policing and may provide insight into how to design better crime prevention strategies, contributing to a broader dialog on homeland security. Simultaneous development of mathematical and simulation models, as well as continuous empirical testing, will provide a guide for the experimental use of these tools in the social sciences, while the broad interdisciplinary foundation of the project will provide a model for collaboration between mathematicians and social scientists.