Modelling the role of correctional services on gangs: Insights through a mathematical model

Abstract

Research has shown that gang membership increases the chances of offending, antisocial behaviour and drug use. Gang membership should be acknowledged as part of crime prevention and policy designs, and when developing interventions and preventative programmes. Correctional services are designed to rehabilitate convicted offenders. We formulate a deterministic mathematical model using nonlinear ordinary differential equations to investigate the role of correctional services on the dynamics of gangs. The recruitment into gang membership is assumed to happen through an imitation process. An epidemic threshold value, Rg, termed the gang reproduction number, is proposed and defined herein in the gangs’ context. The model is shown to exhibit the phenomenon of backward bifurcation. This means that gangs may persist in the population even if Rg is less than one. Sensitivity analysis of Rg was performed to determine the relative importance of different parameters in gang initiation. The critical efficacy ε ∗ is evaluated and the implications of having functional correctional services are discussed.