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, , 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 is less than one. Sensitivity analysis of 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.
Highlights
Correctional services in South Africa provide needs-based correctional sentence plans and interventions that are based on an assessment of the security risk and criminal profile of individuals
We examine which model parameter has the greatest effect on the value of the gang reproduction number Rg
We developed a simple mathematical model to investigate the role of correctional services on gangs
Summary
Correctional services in South Africa provide needs-based correctional sentence plans and interventions that are based on an assessment of the security risk and criminal profile of individuals. Gang violence continues to rise and spread in South Africa. About 25 000 people are released from South Africa prisons and jails each month [6] It is, pertinent to examine the role of correctional centres in controlling or curbing gang activities. Mathematical modelling of gang violence and crimes has been carried out by a number of researchers. An SIR model to analyse recruitment into gangs in a manner reminiscent of spread of infectious disease is given in [10]. Criminal behaviour and violence have been studied as a socially infectious disease, using disease modelling techniques [12,13]. We present a mathematical model which assesses/examines the role of correctional centres in crime reduction.
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