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Dynamics Of Crime Transmission Using Fractional-Order Differential Equations

Author

Listed:
  • KOMAL BANSAL

    (Department of Mathematics, Birla Institute of Technology and Science, Pilani, India)

  • SUGANDHA ARORA

    (Department of Mathematics, Birla Institute of Technology and Science, Pilani, India)

  • KOCHERLAKOTA SATYA PRITAM

    (��School of Technology, Pandit Deendayal Energy University, Gandhi Nagar, India)

  • TRILOK MATHUR

    (Department of Mathematics, Birla Institute of Technology and Science, Pilani, India)

  • SHIVI AGARWAL

    (Department of Mathematics, Birla Institute of Technology and Science, Pilani, India)

Abstract

Due to the alarming rise in types of crime committed and the number of criminal activities across the world, there is a great need to amend the existing policies and models adopted by jurisdictional institutes. The majority of the mathematical models have not included the history of the crime committed by the individual, which is vital to control crime transmission in stipulated time. Further, due to various external factors and policies, a considerable number of criminals have not been imprisoned. To address the aforementioned issues prevailing in society, this research proposes a fractional-order crime transmission model by categorizing the existing population into four clusters. These clusters include law-abiding citizens, criminally active individuals who have not been imprisoned, prisoners, and prisoners who completed the prison tenure. The well-posedness and stability of the proposed fractional model are discussed in this work. Furthermore, the proposed model is extended to the delayed model by introducing the time-delay coefficient as time lag occurs between the individual’s offense and the judgment. The endemic equilibrium of the delayed model is locally asymptotically stable up to a certain extent, after which bifurcation occurs.

Suggested Citation

  • Komal Bansal & Sugandha Arora & Kocherlakota Satya Pritam & Trilok Mathur & Shivi Agarwal, 2022. "Dynamics Of Crime Transmission Using Fractional-Order Differential Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-16, February.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:01:n:s0218348x22500128
    DOI: 10.1142/S0218348X22500128
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    Citations

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    Cited by:

    1. Bansal, Komal & Mathur, Trilok & Agarwal, Shivi, 2023. "Fractional-order crime propagation model with non-linear transmission rate," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Zehba Raizah & Rahat Zarin, 2023. "Advancing COVID-19 Understanding: Simulating Omicron Variant Spread Using Fractional-Order Models and Haar Wavelet Collocation," Mathematics, MDPI, vol. 11(8), pages 1-30, April.
    3. Zhang, Fangfang & Zhang, Shuaihu & Chen, Guanrong & Li, Chunbiao & Li, Zhengfeng & Pan, Changchun, 2022. "Special attractors and dynamic transport of the hybrid-order complex Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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