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Underlying dynamics of crime transmission with memory

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  • Pritam, Kocherlakota Satya
  • Sugandha,
  • Mathur, Trilok
  • Agarwal, Shivi

Abstract

Various studies suggest different mathematical models of integer order differential equations predict crime. But these models do not inherit non-local property, which depicts behavior changes due to contact with criminals for a long period. To overcome this, a fractional-order mathematical model of crime transmission is proposed in this study. The proposed model considers the previous effects of the input while predicting the crime growth rate. A mathematical model of crime transmission inherited with memory property is proposed in this study to analyze crime congestion. Abstract compartmental parameters of fractional crime transmission equation, which illustrates various stages of criminal activity, were employed to analyze crime contagion in the society. The present study demonstrates the progression of the flow of population by classifying into three systems based on involvement in crime and imprisonment by considering the criminal history of an individual. Subsequently, the equilibria of the three-dimensional fractional crime transmission model are evaluated using phase-plane analysis. The Lyapunov function is employed to determine threshold conditions to achieve a crime-free society.

Suggested Citation

  • Pritam, Kocherlakota Satya & Sugandha, & Mathur, Trilok & Agarwal, Shivi, 2021. "Underlying dynamics of crime transmission with memory," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921001910
    DOI: 10.1016/j.chaos.2021.110838
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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. Wang, Shoou-Jiun & Batta, Rajan & Rump, Christopher M., 2005. "Stability of a crime level equilibrium," Socio-Economic Planning Sciences, Elsevier, vol. 39(3), pages 229-244, September.
    3. Gallegos, Javier A. & Duarte-Mermoud, Manuel A., 2016. "On the Lyapunov theory for fractional order systems," Applied Mathematics and Computation, Elsevier, vol. 287, pages 161-170.
    4. Alfred Blumstein & Richard Larson, 1969. "Models of a Total Criminal Justice System," Operations Research, INFORMS, vol. 17(2), pages 199-232, April.
    5. Luo-Luo Jiang & Matjaž Perc & Attila Szolnoki, 2013. "If Cooperation Is Likely Punish Mildly: Insights from Economic Experiments Based on the Snowdrift Game," PLOS ONE, Public Library of Science, vol. 8(5), pages 1-7, May.
    6. Mamta Mittal & Lalit Mohan Goyal & Jasleen Kaur Sethi & D. Jude Hemanth, 2019. "Monitoring the Impact of Economic Crisis on Crime in India Using Machine Learning," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1467-1485, April.
    7. Aaron Chalfin & Justin McCrary, 2017. "Criminal Deterrence: A Review of the Literature," Journal of Economic Literature, American Economic Association, vol. 55(1), pages 5-48, March.
    8. Freeman, Scott & Grogger, Jeffrey & Sonstelie, Jon, 1996. "The Spatial Concentration of Crime," Journal of Urban Economics, Elsevier, vol. 40(2), pages 216-231, September.
    9. Turner, Mary & Peacock, Marian & Payne, Sheila & Fletcher, Andrew & Froggatt, Katherine, 2018. "Ageing and dying in the contemporary neoliberal prison system: Exploring the ‘double burden’ for older prisoners," Social Science & Medicine, Elsevier, vol. 212(C), pages 161-167.
    10. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    11. Ullah, Saif & Altaf Khan, Muhammad & Farooq, Muhammad, 2018. "A fractional model for the dynamics of TB virus," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 63-71.
    12. Bijan Berenji & Tom Chou & Maria R D'Orsogna, 2014. "Recidivism and Rehabilitation of Criminal Offenders: A Carrot and Stick Evolutionary Game," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-13, January.
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