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

Author

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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
    Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK)

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.

Suggested Citation

  • Tichaona Chikore & Farai Nyabadza & K. A. Jane White, 2023. "Exploring the Impact of Nonlinearities in Police Recruitment and Criminal Capture Rates: A Population Dynamics Approach," Mathematics, MDPI, vol. 11(7), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1669-:d:1112240
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    References listed on IDEAS

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    1. Maria Cracolici & Teodora Uberti, 2009. "Geographical distribution of crime in Italian provinces: a spatial econometric analysis," Review of Regional Research: Jahrbuch für Regionalwissenschaft, Springer;Gesellschaft für Regionalforschung (GfR), vol. 29(1), pages 1-28, February.
    2. Chao Zhang & Shahrzad Gholami & Debarun Kar & Arunesh Sinha & Manish Jain & Ripple Goyal & Milind Tambe, 2016. "Keeping Pace with Criminals: An Extended Study of Designing Patrol Allocation against Adaptive Opportunistic Criminals," Games, MDPI, vol. 7(3), pages 1-27, June.
    3. Soumya Banerjee & Pascal Van Hentenryck & Manuel Cebrian, 2015. "Competitive dynamics between criminals and law enforcement explains the super-linear scaling of crime in cities," Palgrave Communications, Palgrave Macmillan, vol. 1(palcomms2), pages 15022-15022, September.
    4. Cheng‐Kuang Wu & Yi‐Ming Chen & Dachrahn Wu & Ching‐Lin Chi, 2020. "A Game Theory Approach for Assessment of Risk and Deployment of Police Patrols in Response to Criminal Activity in San Francisco," Risk Analysis, John Wiley & Sons, vol. 40(3), pages 534-549, March.
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    Cited by:

    1. Sooknanan, Joanna & Seemungal, Terence A.R., 2023. "Criminals and their models - a review of epidemiological models describing criminal behaviour," Applied Mathematics and Computation, Elsevier, vol. 458(C).

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