A dynamic economic model of criminal activity  in the criminal law

Chaharborj, Fatemeh Seddighi; Pourghahramani, Babak; Chaharborj, Sarkhosh Seddighi

doi:10.14419/ijbas.v6i4.7969

IJBAS

2017

DOI: 10.14419/ijbas.v6i4.7969

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A dynamic economic model of criminal activity in the criminal law

Fatemeh Seddighi Chaharborj¹,

Babak Pourghahramani²,

Sarkhosh Seddighi Chaharborj

Abstract: Poverty and crime are two major problem areas. The economic theory of crime shows a direct correlation between poverty and crime. In this study, we propose a model that shows the correlation between poverty and crime. Then we obtain the dynamic system of the proposed model. In the next step, we will compute the reproductive number by finding the maximum eigenvalue of Jacobian matrix to study of stability and un-stability of the presented model.

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A Study of Fractional Order Financial Crime Model Using the Gegenbauer Wavelet Collocation Method

2024

Advcd Theory and Sims

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The manuscript investigates the numerical approximation of the fractional mathematical model of the financial crime population dynamics by the Gegenbauer wavelet collocation method. The study aims to enhance the accuracy and efficiency of solving the underlying differential equations that describe these phenomena by utilizing the proposed technique. The financial crime model is a nonlinear coupled system of ordinary differential equations. Using the Gegenbauer wavelets, the novel operational matrices of integration are created. A nonlinear system of ordinary differential equations are transformed into a system of algebraic equations using the characteristics of the Gegenbauer wavelet expansions and the operational matrix of integration, which speeds up processing. Then, this system of algebraic equations is solved using the Newton‐iterative technique to find the unknown Gegenbauer coefficients that help to obtain the approximate solution for the system. A numerical illustration is presented to show the efficacy and precision of the approach. The numerical results obtained from the projected approach are compared with the existing methods, such as NDSolve and Runge Kutta methods. These results show that the projected scheme is simple, reliable, and resilient. The findings suggest that this approach can be a powerful tool for researchers and practitioners in the financial sector, aiding in developing crime prevention and intervention strategies. The study concludes with suggestions for future research directions.

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A Study of Fractional Order Financial Crime Model Using the Gegenbauer Wavelet Collocation Method

2024

Advcd Theory and Sims

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Modelling financial crime population dynamics: optimal control and cost-effectiveness analysis

Akanni¹,

Akinpelu

Olaniyi

et al. 2019

Int. J. Dynam. Control

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Computational modeling of financial crime population dynamics under different fractional operators

Zarin

Raouf

Khan

et al. 2023

MATH

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<abstract><p>This paper presents an analysis and numerical simulation of financial crime population dynamics using fractional order calculus and Newton's polynomial. The dynamics of financial crimes are modeled as a fractional-order system, which is then solved using numerical methods based on Newton's polynomial. The results of the simulation provide insights into the behavior of financial crime populations over time, including the stability and convergence of the systems. The study provides a new approach to understanding financial crime populations and has potential applications in developing effective strategies for combating financial crimes. Fractional derivatives are commonly applied in many interdisciplinary fields of science because of its effectiveness in understanding and analyzing complicated phenomena. In this work, a mathematical model for the population dynamics of financial crime with fractional derivatives is reformulated and analyzed. A fractional-order financial crime model using the new Atangana-Baleanu-Caputo (ABC) derivative is introduced. The reproduction number for financial crime is calculated. In addition, the relative significance of model parameters is also determined by sensitivity analysis. The existence and uniqueness of the solution in consideration of the ABC derivative are discussed. A number of conditions are established for the existence and Ulam-Hyers stability of financial crime equilibria. A numerical scheme is presented for the proposed model, starting with the Caputo-Fabrizio fractional derivative, followed by the Caputo and Atangana-Baleanu fractional derivatives. Finally, we solve the models with fractal-fractional derivatives.</p></abstract>

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A dynamic economic model of criminal activity in the criminal law

Cited by 3 publications

References 1 publication

A Study of Fractional Order Financial Crime Model Using the Gegenbauer Wavelet Collocation Method

A Study of Fractional Order Financial Crime Model Using the Gegenbauer Wavelet Collocation Method

Modelling financial crime population dynamics: optimal control and cost-effectiveness analysis

Computational modeling of financial crime population dynamics under different fractional operators

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