Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 107, Issue 9, Pages 3961-3965Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.0910921107
Keywords
crime pattern formation; hotspot policing; mathematical modeling; nonlinearity; partial differential equations
Categories
Funding
- US National Science Foundation [BCS-0527388]
- NSF Mathematics [DMS-0907931]
- Office of Naval Research [N000141010221]
- Army Research Office [W911NS-09-1-0559, 50363-MA-MUR]
- Direct For Mathematical & Physical Scien [0968309] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [0968309] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0907931] Funding Source: National Science Foundation
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The mechanisms driving the nucleation, spread, and dissipation of crime hotspots are poorly understood. As a consequence, the ability of law enforcement agencies to use mapped crime patterns to design crime prevention strategies is severely hampered. We also lack robust expectations about how different policing interventions should impact crime. Here we present a mathematical framework based on reaction-diffusion partial differential equations for studying the dynamics of crime hotspots. The system of equations is based on empirical evidence for how offenders move and mix with potential victims or targets. Analysis shows that crime hotspots form when the enhanced risk of repeat crimes diffuses locally, but not so far as to bind distant crime together. Crime hotspots may form as either supercritical or subcritical bifurcations, the latter the result of large spikes in crime that override linearly stable, uniform crime distributions. Our mathematical methods show that subcritical crime hotspots may be permanently eradicated with police suppression, whereas supercritical hotspots are displaced following a characteristic spatial pattern. Our results thus provide a mechanistic explanation for recent failures to observe crime displacement in experimental field tests of hotspot policing.
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