Case Study 1 M. B. Short, M. R. D’Orsogna, V. B., G. E. Tita, P. J. Brantingham, A. L. Bertozzi and L. B. Chayes, Math. Models and Methods in Applied Sciences, Vol 18, (2008) A Statistical Model of Criminal Behaviour

The spreading of disorder: K. Keizer, S. Lindenberg, and L. Steg, Science (2008) Crime is complex

Bowers, Johnson, Domestic Burglary Repeats and Space-Time Clusters. European journal of criminology (2004) Repeat Victimisation

Appear at rate which is constant through space Decides to burgle site with probability: If the criminal agent chooses not to burgle the current location, it moves to a neighbouring house with probability: Otherwise – if the criminal agent decides to burgle, it will then leave the system, and affect the attractiveness of the victimised site The Discrete Model Two dimensional lattice, grid spacing l Attractiveness: If a site is burgled, the dynamic component of attractiveness is adjusted as follows: Homes, s = (i,j) Burglars Static component Dynamic component

The Discrete Model M. B. Short et al Math.Models and Methods in App. Sci, Vol 18, (2008)

New burglar generated A = 1 A = 3 q = 1/6 q = 3/6 Assesses attractiveness of neighbouring sites Moves probabilistically Burglar removed from the system Dynamic attractiveness of local sites increase B(t)

The Discrete Model With thanks to Toby Davies