DYNAMICS OF CRIME TRANSMISSION USING FRACTIONAL-ORDER DIFFERENTIAL EQUATIONS

Komal Bansal (), Sugandha Arora, Kocherlakota Satya Pritam (), Trilok Mathur () and Shivi Agarwal ()
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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

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-16

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.

Keywords: Fractional Differential Equation; Crime Transmission; Delay Model; Mathematical Modeling (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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DOI: 10.1142/S0218348X22500128

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