Mathematicians suggest ways to deal with criminal hotspots

Published 25 February 2010

Mathematicians suggest that there are two kinds of crime hotspots: “supercritical” and “subcritical”; the mathematicians’ equations indicated that rigorous policing could completely eliminate the subcritical hotspots, but would simply displace the supercritical variety

Jeffrey Brantingham of the University of California, Los Angeles, and his colleagues set out to calculate how the movements of criminals and victims create opportunities for crime, and how police can reduce it. Peter Aldhous writes that they came up with a pair of equations that could explain how local crime hotspots form — which turned out to be similar to those that describe molecular reactions and diffusion.

The equations suggested there are two kinds of hotspot:

  • The first, called “supercritical,” arises when small spikes in crime pass a certain threshold and create a local crime wave.
  • The second, “subcritical,” happens when a particular factor — the presence of a drug den, for instance — causes a large spike in crime.

The equations also indicated that rigorous policing could completely eliminate the subcritical hotspots, but would simply displace the supercritical variety.

The approach “presents a novel hypothesis of how hotspots form”, says John Eck, a criminologist at the University of Cincinnati, Ohio. Brantingham hopes eventually to be able to predict where subcritical hotspots are forming, so police can step in to nip problems in the bud. His team is already collaborating with Los Angeles< police.

-read more in Martin B. Short et al., “Dissipation and Displacement of Hotspots in Reaction-Diffusion Models of Crime,” Proceedings of the National Academy of Sciences (5 January 2010) (DOI: 10.1073/pnas.0910921107)