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A mathematical model of serious and minor criminal activity

Published online by Cambridge University Press:  08 April 2016

A. A. LACEY  and
M. N. TSARDAKAS
A. A. LACEY
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS, UK email: a.a.Lacey@hw.ac.uk, mtsardakas@gmail.com
M. N. TSARDAKAS
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS, UK email: a.a.Lacey@hw.ac.uk, mtsardakas@gmail.com
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Abstract

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Using mathematical methods to understand and model crime is a recent idea that has drawn considerable attention from researchers during the last five years. From the plethora of models that have been proposed, perhaps the most successful one has been a diffusion-type differential equations model that describes how the number of criminals evolves in a specific area. We propose a more detailed form of this model that allows for two distinct criminal types associated with major and minor crime. Additionally, we examine a stochastic variant of the model that represents more realistically the ‘generation’ of new criminals. Numerical solutions from both models are presented and compared with actual crime data for the Greater Manchester area. Agreement between simulations and actual data is satisfactory. A preliminary statistical analysis of the data also supports the model's potential to describe crime.

Keywords

Crimedifferential equationsmathematical model
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 3: Mathematical Modelling of Crime and Security , June 2016 , pp. 403 - 421
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Cambridge University Press 2016

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