Modeling and control of crime using optimal control theory

Abstract

This research introduces a compartmental mathematical model, inspired by epidemiology, to analyze crime dynamics and design reduction strategies. The population is divided into four groups: susceptible individuals, active criminals, prisoners, and rehabilitated individuals. Two control functions are incorporated: one aimed at deterrence through sanction policies, and the other focused on social reintegration via educational, psychological, and professional support programs. Based on optimal control theory, the model identifies relevant intervention strategies to prevent crime and improve its management. The theoretical findings are validated through numerical simulations using MATLAB, comparing the system’s evolution with and without intervention. This approach offers a solid analytical framework to support the development of integrated, flexible, and adaptive public policies addressing contemporary crime-related challenges.