IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v567y2021ics0378437120310232.html
   My bibliography  Save this article

Dynamical analysis and effects of law enforcement in a social interaction model

Author

Listed:
  • Tripathi, Jai Prakash
  • Bugalia, Sarita
  • Burdak, Kavita
  • Abbas, Syed

Abstract

Crime is a rising problem all over the world. Over the years, several researches have been conducted to coin suitable model systems and intervention strategies that would decrease delinquent behavior and promote prosocial development. Being dynamic and complex process, the spread of crime requires a system level approach. In this paper, we formulate and analyze a series of dynamical model systems of the dilation of crime incorporating law enforcement. The population models of social interactions have been constructed based on predator–prey interaction models with Holling type II response function. Two different types of populations (criminal minded and non-criminal minded) have been assumed in the given community/society. According to law policy for crime control, we scrutinize the dynamic behavior of the model system concerning law enforcement on the criminal minded population. Along with analytical expressions for the existence of different equilibrium points and their stability, we have also provided their geometrical interpretations using isocline analysis. The expressions obtained for the existence and stability of equilibrium points have been used to investigate the effects of coefficient of law enforcement and the logistic growth term on the prevalence of crime. It is observed that for a threshold value of law enforcement, a stable limit cycle exists. In particular, a threshold of law enforcement is determined beyond which the associated place/community could be made crime free. A threshold value R0 (similar to basic reproduction number in epidemiology) has also been introduced. It is shown that when R0<1, crime free equilibrium is stable. The elimination and persistence of crime have been discussed via two parameters (law enforcement and half saturation constant) bifurcation diagram. Theoretical results have been supported via numerical simulations followed by discussion and societal impacts of the present study.

Suggested Citation

  • Tripathi, Jai Prakash & Bugalia, Sarita & Burdak, Kavita & Abbas, Syed, 2021. "Dynamical analysis and effects of law enforcement in a social interaction model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    • Handle: RePEc:eee:phsmap:v:567:y:2021:i:c:s0378437120310232
    DOI: 10.1016/j.physa.2020.125725
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437120310232
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2020.125725?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gary S. Becker, 1974. "Crime and Punishment: An Economic Approach," NBER Chapters, in: Essays in the Economics of Crime and Punishment, pages 1-54, National Bureau of Economic Research, Inc.
    2. Entorf, Horst & Spengler, Hannes, 2000. "Socioeconomic and demographic factors of crime in Germany: Evidence from panel data of the German states," International Review of Law and Economics, Elsevier, vol. 20(1), pages 75-106, March.
    3. Iglesias, J.R. & Semeshenko, V. & Schneider, E.M. & Gordon, M.B., 2012. "Crime and punishment: Does it pay to punish?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3942-3950.
    4. Lin, Ming-Jen, 2009. "More police, less crime: Evidence from US state data," International Review of Law and Economics, Elsevier, vol. 29(2), pages 73-80, June.
    5. Junichi Minagawa, 2007. "A Determinantal Criterion of Hopf Bifurcations and Its Application to Economic Dynamics," Springer Books, in: Toichiro Asada & Toshiharu Ishikawa (ed.), Time and Space in Economics, chapter 9, pages 161-172, Springer.
    6. Wim Bernasco & Thomas de Graaff & Jan Rouwendal & Wouter Steenbeek, 2017. "Social Interactions and Crime Revisited: An Investigation Using Individual Offender Data in Dutch Neighborhoods," The Review of Economics and Statistics, MIT Press, vol. 99(4), pages 622-636, July.
    7. Passell, Peter & Taylor, John B, 1977. "The Deterrent Effect of Capital Punishment: Another View," American Economic Review, American Economic Association, vol. 67(3), pages 445-451, June.
    8. Ehrlich, Isaac, 1975. "The Deterrent Effect of Capital Punishment: A Question of Life and Death," American Economic Review, American Economic Association, vol. 65(3), pages 397-417, June.
    9. Tiwari, Vandana & Tripathi, Jai Prakash & Mishra, Swati & Upadhyay, Ranjit Kumar, 2020. "Modeling the fear effect and stability of non-equilibrium patterns in mutually interfering predator–prey systems," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    10. Edward L. Glaeser & Bruce Sacerdote & José A. Scheinkman, 1996. "Crime and Social Interactions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 111(2), pages 507-548.
    11. Steven D. Levitt, 1996. "The Effect of Prison Population Size on Crime Rates: Evidence from Prison Overcrowding Litigation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 111(2), pages 319-351.
    12. Malthus, Thomas Robert, 1798. "An Essay on the Principle of Population," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number malthus1798.
    13. Alves, Luiz G.A. & Ribeiro, Haroldo V. & Mendes, Renio S., 2013. "Scaling laws in the dynamics of crime growth rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(11), pages 2672-2679.
    14. R. M. Goodwin, 1982. "A Growth Cycle," Palgrave Macmillan Books, in: Essays in Economic Dynamics, chapter 12, pages 165-170, Palgrave Macmillan.
    15. Nuño, Juan C. & Herrero, Miguel A. & Primicerio, Mario, 2008. "A triangle model of criminality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2926-2936.
    16. R. M. Goodwin, 1982. "Essays in Economic Dynamics," Palgrave Macmillan Books, Palgrave Macmillan, number 978-1-349-05504-3, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Bansal, Komal & Mathur, Trilok & Agarwal, Shivi, 2023. "Fractional-order crime propagation model with non-linear transmission rate," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guido Travaglini, 2003. "Property Crime and Law Enforcement in Italy. A Regional Panel Analysis 1980-95," Giornale degli Economisti, GDE (Giornale degli Economisti e Annali di Economia), Bocconi University, vol. 62(2), pages 211-240, October.
    2. Luiz G A Alves & Haroldo V Ribeiro & Ervin K Lenzi & Renio S Mendes, 2013. "Distance to the Scaling Law: A Useful Approach for Unveiling Relationships between Crime and Urban Metrics," PLOS ONE, Public Library of Science, vol. 8(8), pages 1-8, August.
    3. Alves, Luiz G.A. & Ribeiro, Haroldo V. & Rodrigues, Francisco A., 2018. "Crime prediction through urban metrics and statistical learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 435-443.
    4. Paul R. Zimmerman, 2010. "The Economics of Capital Punishment and Deterrence," Chapters, in: Bruce L. Benson & Paul R. Zimmerman (ed.), Handbook on the Economics of Crime, chapter 16, Edward Elgar Publishing.
    5. Fajnzylber, Pablo & Lederman, Daniel & Loayza, Norman, 2002. "What causes violent crime?," European Economic Review, Elsevier, vol. 46(7), pages 1323-1357, July.
    6. Lauridsen, Jørgen & Nannerup, Niels & Skak, Morten, 2013. "Does Owner-Occupied Housing Affect Neighbourhood Crime?," Discussion Papers on Economics 19/2013, University of Southern Denmark, Department of Economics.
    7. Blesse, Sebastian & Diegmann, André, 2019. "Police reorganization and crime: Evidence from police station closures," Working Papers 07/2019, German Council of Economic Experts / Sachverständigenrat zur Begutachtung der gesamtwirtschaftlichen Entwicklung.
    8. Crinò, Rosario & Immordino, Giovanni & Piccolo, Salvatore, 2019. "Marginal deterrence at work," Journal of Economic Behavior & Organization, Elsevier, vol. 166(C), pages 586-612.
    9. Anna Bonanno, 2006. "The economic analysis of offender’s choice: Old and new insights," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 53(2), pages 193-224, June.
    10. Abbas, Syed & Tripathi, Jai Prakash & Neha, A.A., 2017. "Dynamical analysis of a model of social behavior: Criminal vs non-criminal population," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 121-129.
    11. O’Flaherty, Brendan & Sethi, Rajiv, 2015. "Urban Crime," Handbook of Regional and Urban Economics, in: Gilles Duranton & J. V. Henderson & William C. Strange (ed.), Handbook of Regional and Urban Economics, edition 1, volume 5, chapter 0, pages 1519-1621, Elsevier.
    12. Adolfo Sachsida & Mario Mendonça & Paulo Loureiro & Maria Gutierrez, 2010. "Inequality and criminality revisited: further evidence from Brazil," Empirical Economics, Springer, vol. 39(1), pages 93-109, August.
    13. Rodrigo Vergara., 2009. "Crime Prevention Programs: Evidence for a Developing Country," Documentos de Trabajo 362, Instituto de Economia. Pontificia Universidad Católica de Chile..
    14. George Saridakis & Sandra Sookram, 2014. "Violent Crime and Perceived Deterrence: An Empirical Approach using the Offending Crime and Justice Survey," Economic Issues Journal Articles, Economic Issues, vol. 19(1), pages 23-56, March.
    15. Alves, Luiz G.A. & Ribeiro, Haroldo V. & Mendes, Renio S., 2013. "Scaling laws in the dynamics of crime growth rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(11), pages 2672-2679.
    16. Entorf, Horst & Spengler, Hannes, 2000. "Socioeconomic and demographic factors of crime in Germany: Evidence from panel data of the German states," International Review of Law and Economics, Elsevier, vol. 20(1), pages 75-106, March.
    17. Entorf, H. & Winker, P., 2008. "Investigating the drugs-crime channel in economics of crime models: Empirical evidence from panel data of the German States," International Review of Law and Economics, Elsevier, vol. 28(1), pages 8-22, March.
    18. Blesse, Sebastian & Diegmann, André, 2022. "The place-based effects of police stations on crime: Evidence from station closures," Journal of Public Economics, Elsevier, vol. 207(C).
    19. Emeline Bezin & Thierry Verdier & Yves Zenou, 2022. "Crime, Broken Families, and Punishment," American Economic Journal: Microeconomics, American Economic Association, vol. 14(4), pages 723-760, November.
    20. Steven D. Levitt, 1998. "Juvenile Crime and Punishment," Journal of Political Economy, University of Chicago Press, vol. 106(6), pages 1156-1185, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:567:y:2021:i:c:s0378437120310232. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.