On Mathematical Study of Juvenile Delinquency with Precautionary Measure, Public Education and Intervention Programs as Control Strategies

Abstract

In this paper, we develop a mathematical model for juvenile delinquency transmission dynamics by incorporating key control strategies, namely precautionary measures, public education, and intervention programs. The model aims to identify effective prevention and control measures for curbing the spread of delinquent behavior among youths, with particular emphasis on evaluating the efficacy of public education. Adopting an epidemiological modelling framework, we derive a system of nonlinear differential equations governing the dynamics of juvenile delinquency over time. Stability analysis of the model is conducted, and the basic reproduction number along with the equilibrium points for both delinquency-free and endemic scenarios are established. Numerical simulations reveal that controlling the entry rate of juveniles into the population, reducing the transition rate from susceptible to delinquent status, and minimizing the rate at which individuals return to delinquency from correctional centers are critical for mitigating the spread of delinquent behavior. Moreover, while public education shows limited impact among susceptible individuals, it proves highly effective among the exposed, delinquent, and those in correctional facilities. Enhanced public education on the consequences of delinquency also contributes to reducing both arrest rates and juvenile homicides. This work offers valuable insights for researchers in applied mathematics, behavioral science, and healthcare management, while providing evidence-based guidance for policymakers seeking to manage and control juvenile delinquency.