A compartmental modeling of crime influenced by drug consumption

Abstract

This article proposes a discrete compartmental model to analyze the influence of drug consumption on crime dynamics and to assess the effectiveness of different intervention strategies. The population is divided into five categories: susceptible individuals, drug users, active criminals, prisoners, and rehabilitated individuals. Three control functions are introduced: rehabilitation of drug users, social reintegration of rehabilitated individuals, and awareness campaigns. Based on optimal control theory and Pontryagin’s maximum principle, the necessary conditions for identifying optimal strategies are established. Numerical simulations carried out using MATLAB complement the theoretical analysis and illustrate the behavior of the system with and without intervention.