Exploring the Impact of Nonlinearities in Police Recruitment and Criminal Capture Rates: A Population Dynamics Approach

Tichaona Chikore, Farai Nyabadza and K. A. Jane White ()
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Tichaona Chikore: Department of Applied Mathematics, University of Johannesburg, Johannesburg 2006, South Africa
Farai Nyabadza: Department of Applied Mathematics, University of Johannesburg, Johannesburg 2006, South Africa
K. A. Jane White: Department of Applied Mathematics, University of Johannesburg, Johannesburg 2006, South Africa

Mathematics, 2023, vol. 11, issue 7, 1-13

Abstract: The interplay between criminal activity and crime control/prevention measures is inherently dynamic. This paper presents a simple nonlinear dynamical system in which criminal activity levels are coupled to policing effort. Through the process of non-dimensionalisation and sensitivity analysis, policing efficiency and the responsiveness of policing effort are identified as key parameter groupings. An analysis of the system shows that bi-stability is a feature of the dynamics. When there is no feedback between criminal activity and police recruitment, a saddle-node bifurcation occurs and threshold levels of criminal activity are required for the activity to be maintained. When feedback is permitted, we also find a backward bifurcation and criminal activity can be contained for policing efficiency below its threshold level. We demonstrate proof of concept for how the model might be used as a predictive tool with real data.

Keywords: mathematical criminology; criminal activity; police effort; policing efficiency; dynamical system; bifurcations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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