Mathematical Modeling of Criminal Activities: An Approach Based on Homotopy Perturbations

Snežana Stojičić; Vladica Stojanović; Radovan Radovanović; Dušan Joksimović; Mihailo Jovanović

doi:10.59400/adecp3329

Mathematical Modeling of Criminal Activities: An Approach Based on Homotopy Perturbations

Snežana Stojičić Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11000 Belgrade, Serbia
Vladica Stojanović Department of Informatics & Computer Sciences University of Criminal Investigation and Police Studies
Radovan Radovanović Department of Forensic Sciences, University of Criminal Investigation and Police Studies, 11000 Belgrade, Serbia
Dušan Joksimović Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11000 Belgrade, Serbia
Mihailo Jovanović Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11000 Belgrade, Serbia

Article ID: 3329

DOI: https://doi.org/10.59400/adecp3329

Keywords: Crime modeling; coupled differential equations; homotopy perturbations; convergence; simulation; application

Abstract

The manuscript deals with solving a mathematical model of criminal activities (MCA model) in order to facilitate the understanding of the dynamics of crime and implement certain measures in its prevention and deterrence. For the MCA model, which consists of two coupled ordinary differential equations of the diffusion type, the stability and existence of a unique Cauchy solution are first examined. Thereafter, coupled equations of the MCA model are transformed into a dimensionless system on the unit interval and solved using the homotopy perturbation method (HPM). In this way, recursive sequences of approximate HPM solutions are obtained, and, under certain conditions, their convergence has been proven. In the following, using different initial conditions, several numerical simulations of the proposed HPM technique in solving the MCA model were conducted, as well as a practical application of the proposed procedure in modelling real-world crime rate data.

Published

2025-09-30

How to Cite

Stojičić, S., Stojanović, V., Radovanović, R., Joksimović, D., & Jovanović, M. (2025). Mathematical Modeling of Criminal Activities: An Approach Based on Homotopy Perturbations. Advances in Differential Equations and Control Processes, 32(3). https://doi.org/10.59400/adecp3329

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Issue

Vol. 32 No. 3 (2025)

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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