Model Matematika Terhadap Dinamika Kriminalitas di Provinsi Sumatera Utara
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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