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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: [email protected]
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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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References

[1]Beavon, D. J. K., Brantingham, P. L. & Brantingham, P. J. (1994) The influence of street networks on the patterning of property offenses. In: Clarke, R. V. (editor) Crime Prevention Studies, 1st edn., Criminal Justice Press, vol. 2, pp. 115–148.Google Scholar
[2]Bernasco, W. (2008) Them again: Same offender involvement in repeat and near repeat burglaries. Eur. J. Criminol. 5, 411–431.CrossRefGoogle Scholar
[3]Bowers, K. J. & Johnson, S. D. (2005) Domestic burglary repeats and space-time clusters: the dimensions of risk. Eur. J. Criminol. 2, 67–92.CrossRefGoogle Scholar
[4]Braga, A. A. (2001) The effects of hot spots policing on crime. Ann. Am. Acad. Polit. Soc. Sci. 578, 104–125.CrossRefGoogle Scholar
[5]Ericsson, U. (1995) Straight from the horse's mouth. Forensic Update 43, 23–25.Google Scholar
[6]Johnson, S. D., Bernasco, W., Bowers, K. J., Elffers, H., Ratcliffe, J., Rengert, G. & Townsley, M. (2007) Space-time patterns of risk: A cross national assessment of residential burglary victimization. J. Quant. Criminol. 23, 201–219.CrossRefGoogle Scholar
[7]Johnson, S. D., Summers, L. & Pease, K. (2009) Offender as forager? A direct test of the boost account of victimization. J. Quant. Criminol. 25, 181–200.CrossRefGoogle Scholar
[8]Koper, C. S. (1995) Just enough police presence: Reducing crime and disorderly behavior by optimizing patrol in crime hot spots. Justice Q. 12 (4), 649–672.CrossRefGoogle Scholar
[9]Murray, J. D. (2003) Mathematical Biology II: Spatial Models and Biomedical Applications, 3rd edn., Springer.CrossRefGoogle Scholar
[10]Sherman, L. W. & Weisburd, D. (1995) General deterrent effects of police patrol in crime “hot spots”: A randomized, controlled trial. Justice Q. 12, 625–648.CrossRefGoogle Scholar
[11]Short, M. B., D'Orsogna, M. R., Pasour, V. B., Tita, G. E., Brantingham, P. J., Bertozzi, A. L. & Chayes, L. B. (2008) A statistical model of criminal behavior. Math. Models Methods Appl. Sci. 18, 1249–1267.CrossRefGoogle Scholar
[12]Summers, L., Johnson, S. D. & Rengert, G. F. (2010) The use of maps in offender interviewing. In: Bernasco, W. (editor) Offenders on Offending: Learning About Crime from Criminals, 1st edn., Willan, Cullompton, pp. 246–272.Google Scholar
[13]Townsley, M., Homel, R. & Chaseling, J. (2000) Repeat burglary victimisation: Spatial and temporal patterns. Aust. N.Z. J. Criminol. 33, 37–63.CrossRefGoogle Scholar
[14]Walker, J. T. (2007) Advancing science and research in criminal justice/criminology: Complex systems theory and non-linear analyses. Justice Q. 24, 555–581.CrossRefGoogle Scholar
[15]Weisburd, D., Wyckoff, L. A., Ready, J., Eck, J. E., Hinkle, J. C. & Gajewski, F. (2006) Does crime just move around the corner? A controlled study of spatial displacement and diffusion of crime control benefits. Criminology 44, 549–592.CrossRefGoogle Scholar