A mathematical model for the treatment of delinquent behaviour

A key predictor variable for juvenile delinquency is the presence of delinquent peers. Consequently, delinquent behaviour may be treated as a socially infectious disease spread by peer influence and its spread modelled using a compartmental model from mathematical epidemiology. A Public Health Approach was used to design the model and this system was found to have three equilibrium states - two with no serious delinquents (non-status offenders) and one with both serious delinquents and status offenders coexisting. We employed a sensitivity analysis on the basic Reproductive number R0, and identified the parameters that should be targeted by treatment strategies to curb the spread of juvenile delinquency. This model may be used by policy makers to provide insights to inform policy creation as well as to set tangible targets for the proportion of delinquents treated and the detention rate.