Towards understanding crime dynamics in a heterogeneous environment: A mathematical approach

K. A. Jane White, Eduard Campillo-Funollet, Farai Nyabadza, Davide Cusseddu, Christian Kasumo, Nancy Matendechere Imbusi, Victor Ogesa Juma, A. J. Meir, Theresia Marijani

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
JournalJournal of Interdisciplinary Mathematics
Early online date25 May 2021
DOIs
Publication statusE-pub ahead of print - 25 May 2021

Keywords

  • 91C99
  • Cape Town
  • Criminal activity and number of criminals
  • Criminal efficiency
  • Mathematical model
  • South Africa

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this