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, 1249-1267(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, 1249-1267(2008)

New burglar generated

A = 1

A = 1

A = 1

A = 3

q = 1/6

q = 1/6

q = 1/6

q = 3/6

Assesses attractiveness of neighbouring sitesMoves probabilisticallyBurglar removed from the systemDynamic attractiveness of local sites increase

B(t)

B(t)

B(t)

B(t)

B(t)

The Discrete Model

With thanks to Toby Davies