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Adding police to a mathematical model of burglary

Published online by Cambridge University Press:  21 April 2010

ASHLEY B. PITCHER
ASHLEY B. PITCHER*
Affiliation:
OCIAM, Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK CAMS-EHESS, Maison des Sciences de l'Homme, 54 bd Raspail, Paris 75006, France email: ashley.pitcher@balliol.oxon.org
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Abstract

We review the Short model of urban residential burglary derived from taking the continuum limit of two difference equations – one of which models the attractiveness of individual houses to burglary, and the other of which models burglar movement. This leads to a system of non-linear partial differential equations. We propose a change to the Short model and also add deterrence caused by the presence of uniformed officers to the model. We solve the resulting system of non-linear partial differential equations numerically and present results both with and without deterrence.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 21 , Issue 4-5: Criminality , October 2010 , pp. 401 - 419
Copyright
Copyright © Cambridge University Press 2010

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