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A fractional-order model to study the dynamics of the spread of crime

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dc.contributor.author Mathur, Trilok
dc.contributor.author Tiwari, Kamlesh
dc.date.accessioned 2024-05-20T10:12:44Z
dc.date.available 2024-05-20T10:12:44Z
dc.date.issued 2023-07
dc.identifier.uri https://www.sciencedirect.com/science/article/pii/S0377042723000468
dc.identifier.uri http://dspace.bits-pilani.ac.in:8080/jspui/xmlui/handle/123456789/14948
dc.description.abstract Numerous crucial factors and parameters influence the dynamic process of the spread of crime. Various integer-order differential models have been proposed to capture crime spread. Most of these introduced dynamic systems have not considered the history of the criminal and the impact of crime on society. To address these shortcomings, a fractional-order crime transmission model is proposed in this manuscript considering five different classes law-abiding citizens, non-incarcerated criminals, incarcerated criminals, prison-released and recidivists. The primary focus of the proposed model is to study the effect of recidivism in society and decide the adequate imprisonment for repeat offenders. The existence, uniqueness, non-negativity and boundedness of the solution of the proposed model are examined. The local stability of the equilibrium points is also analysed using Routh–Hurwitz Criteria with Matignon conditions. Further, the threshold condition for the uniform asymptotic stability of the system is evaluated by the Lyapunov stability method. Moreover, the long-term impact of the imprisonment of criminals on society is also examined in the current study. The numerical simulations of the model for a range of fractional orders are obtained using power series expansion method to strengthen the theoretical results. en_US
dc.language.iso en en_US
dc.publisher Elsevier en_US
dc.subject Mathematics en_US
dc.subject Crime transmission modeling en_US
dc.subject Recidivism en_US
dc.subject Caputo’s fractional-order derivative en_US
dc.title A fractional-order model to study the dynamics of the spread of crime en_US
dc.type Article en_US


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