Griya Journal of Mathematics Education and Application
Vol. 6 No. 2 (2026): Juni 2026

Model Matematika Terhadap Dinamika Kriminalitas di Provinsi Sumatera Utara

Rifka Annaria Sibuea (Universitas Negeri Medan)
Tri Andri Hutapea (Universitas Negeri Medan)



Article Info

Publish Date
29 Jun 2026

Abstract

Crime is a social problem that can affect social stability, the economy, and public safety. Factors such as education, social interaction, and economic conditions play an important role in the spread of crime. This study aims to analyze a mathematical model of crime dynamics in North Sumatra Province, which is divided into five sub-populations, namely SC1C2PR (Susceptible, Criminal Suspect, Criminal Defendant, Prison, Recovered), taking into account the influence of education programs. The analysis conducted involves determining the equilibrium point, calculating the basic reproduction number (R0), and analyzing stability using the linearization method and the Routh-Hurwitz criterion. Based on the analysis results, the basic reproduction number R0 > 1 was obtained, so that the model had two equilibrium points, namely an unstable crime-free equilibrium point and a locally asymptotically stable equilibrium point with crime. This condition represents that one criminal can give rise to more than one new criminal individual, so that criminal activity will persist and spread in society until it reaches a stable state of crime. The simulation results show that effective and equitable education programs can reduce crime rates, but they are not sufficient to achieve a crime-free environment without restricting social interaction. Therefore, other programs are needed to reduce crime rates in North Sumatera.

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Journal Info

Abbrev

Griya

Publisher

Subject

Education Mathematics

Description

Griya Journal of Mathematics Education and Application adalah Jurnal Matematika dan Pendidikan Matematika yang dikelola oleh Program Studi S1 Pendidikan Matematika Universitas Mataram. Fokus dan ruang lingkup dari jurnal ini adalah artikel ilmiah baik berupa hasil penelitian, review artikel maupun ...