Recidivism-Driven Persistence in Crime Dynamics: A Comparative S–C–P–R Compartmental Model for Kupang City, Indonesia

Yohanes Yordente Wete; Maria Lobo; Maria Agustina Kleden; Albert Mario Kumanireng

doi:10.37905/euler.v14i2.38389

Recidivism-Driven Persistence in Crime Dynamics: A Comparative S–C–P–R Compartmental Model for Kupang City, Indonesia

Yohanes Yordente Wete, Maria Lobo, Maria Agustina Kleden, Albert Mario Kumanireng

Abstract

Crime remains a significant social problem in Kupang City, which recorded 2,173 criminal cases in the first half of 2024, necessitating a quantitative approach to understand its dynamics. This study aims to construct and analyze mathematical models of crime dynamics in Kupang City by considering the role of recidivism. Two compartmental models (S–C–P–R) are developed: a model with recidivism and a model without recidivism, each formulated as a system of ordinary differential equations. The analysis includes the determination of equilibrium points, the basic reproduction number (R0) using the Next Generation Matrix method, stability analysis via the Jacobian matrix and the Routh–Hurwitz criterion, sensitivity analysis, and numerical simulation using a Nonstandard Finite Difference (NSFD) scheme. Parameter estimation is performed through exponential regression based on crime data from Kupang City for the period 2013–2024. The results show that the model without recidivism yields R0 = 2.3525, indicating that criminal activity will persist and grow over time. The crime-free equilibrium point is locally asymptotically stable when R0 < 1, and sensitivity analysis identifies the transmission rate β as the most influential parameter affecting R0. In the model with recidivism, the feedback loop from the recovered compartment to the criminal compartment causes the crime-free equilibrium point to become unstable, and R0 is not well-defined due to the absence of a clear generational structure. These findings suggest that recidivism significantly complicates crime control and that strategies focused on reducing the transmission rate β are essential for suppressing criminal activity in Kupang City.

Keywords

Criminality; Mathematical Modelling; Recidivism; Stability; Basic Reproduction Number

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DOI: https://doi.org/10.37905/euler.v14i2.38389