Towards Understanding Crime Dynamics in a Heterogeneous Environment: A Mathematical Approach
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Date
2021
Authors
White, Jane K. A.
Campillo-Funollet, Eduard
Nyabadza, Farai
Cusseddu, Davide
Kasumo, Christian
Imbusi, Nancy Matendechere
Juma, Victor Ogesa
Meir, A. J.
Marijani, Theresia
Journal Title
Journal ISSN
Volume Title
Publisher
Taylor & Francis
Abstract
Crime data provides information on the nature and location of the crime but, in
general, does not include information on the number of criminals operating in a region. By
contrast, many approaches to crime reduction necessarily involve working with criminals
or individuals at risk of engaging in criminal activity and so the dynamics of the criminal
population is important. With this in mind, we develop a mechanistic, mathematical model
which combines the number of crimes and number of criminals to create a dynamical system.
Analysis of the model highlights a threshold for criminal efficiency, below which criminal
numbers will settle to an equilibrium level that can be exploited to reduce crime through
prevention. This efficiency measure arises from the initiation of new criminals in response
to observation of criminal activity; other initiation routes - via opportunism or peer pressure
- do not exhibit such thresholds although they do impact on the level of criminal activity
observed. We used data from Cape Town, South Africa, to obtain parameter estimates and
predicted that the number of criminals in the region is tending towards an equilibrium
point but in a heterogeneous manner - a drop in the number of criminals from low crime
neighbourhoods is being offset by an increase from high crime neighbourhoods.
Description
An Article Published in Journal of Interdisciplinary Mathematics
Keywords
Mathematical model, Criminal activity and number of criminals, Criminal efficiency, Cape Town, South Africa
Citation
K. A. Jane White, Eduard Campillo-Funollet, Farai Nyabadza, Davide Cusseddu, Christian Kasumo, Nancy Matendechere Imbusi, Victor Ogesa Juma, A. J. Meir & Theresia Marijani (2021): Towards understanding crime dynamics in a heterogeneous environment: A mathematical approach, Journal of Interdisciplinary Mathematics, DOI: 10.1080/09720502.2020.1860292