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Modeling the impact of civilian firearm ownership in the evolution of violent crimes

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  • Crokidakis, Nuno

Abstract

We propose a simple mathematical model to describe the evolution of violent crimes. For such purpose, we built a model based on ordinary differential equations that take into account the number of violent crimes and the number of legal and illegal guns. The dynamics is governed by probabilities, modeling for example the police action, the risk perception regarding crimes that leads to increase of ownership of legal guns, and so on. Our analytical and numerical results show that, in addition to the rise of criminality due to the presence of illegal guns, the increase of legal guns leads to a fast increase of violent crimes, suggesting that the access of firearms by civilians is not a good option regarding the control of crimes.

Suggested Citation

  • Crokidakis, Nuno, 2022. "Modeling the impact of civilian firearm ownership in the evolution of violent crimes," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    • Handle: RePEc:eee:apmaco:v:429:y:2022:i:c:s0096300322003307
    DOI: 10.1016/j.amc.2022.127256
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    References listed on IDEAS

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    1. Monteiro, L.H.A., 2020. "More guns, less crime? A dynamical systems approach," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    2. Siegel, M. & Negussie, Y. & Vanture, S. & Pleskunas, J. & Ross, C.S. & King, C., III, 2014. "The relationship between gun ownership and stranger and nonstranger firearm homicide rates in the United States, 1981-2010," American Journal of Public Health, American Public Health Association, vol. 104(10), pages 1912-1919.
    3. Pritam, Kocherlakota Satya & Sugandha, & Mathur, Trilok & Agarwal, Shivi, 2021. "Underlying dynamics of crime transmission with memory," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. Siegel, M. & Ross, C.S. & King III, C., 2013. "The relationship between gun ownership and firearm homicide rates in the United States, 1981-2010," American Journal of Public Health, American Public Health Association, vol. 103(11), pages 2098-2105.
    5. Bree J. Lang & Matthew Lang, 2021. "Pandemics, Protests, and Firearms," American Journal of Health Economics, University of Chicago Press, vol. 7(2), pages 131-163.
    6. Kleck, Gary, 2015. "The Impact of Gun Ownership Rates on Crime Rates: A Methodological Review of the Evidence," Journal of Criminal Justice, Elsevier, vol. 43(1), pages 40-48.
    7. Hamlin, Daniel, 2021. "Are gun ownership rates and regulations associated with firearm incidents in American schools? A forty-year analysis (1980–2019)," Journal of Criminal Justice, Elsevier, vol. 76(C).
    8. Taylor, Benjamin & Li, Jing, 2015. "Do fewer guns lead to less crime? Evidence from Australia," International Review of Law and Economics, Elsevier, vol. 42(C), pages 72-78.
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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).
    2. Crokidakis, Nuno, 2024. "Nonequilibrium phase transitions and absorbing states in a model for the dynamics of religious affiliation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 643(C).

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