Modelling the dark side of prison dynamics: Quantifying the criminogenic effects of petty crime offenders’ incarceration

Crime remains a persistent socio-economic challenge in South Africa, where the incarceration of petty offenders often exacerbates criminal behaviour. Empirical evidence suggests custodial sentencing for minor offences may accelerate progression to serious crime due to exposure to hardened offenders and criminogenic prison conditions. To investigate this, we develop a compartmental ODE model tracking eight population states: susceptibility, petty and serious crime, custodial and non-custodial sentencing, rehabilitation, and relapse pathways. In particular, the model has an explicit non-custodial sentencing compartment, positioned in a distinct community-supervision stratum that is neither the general community nor the prison system, enabling direct comparison of custodial and non-custodial policy scenarios. The model is parameterised using the South African crime and prison data. Sensitivity analysis shows that sentencing rates, rehabilitation efficacy, and relapse probabilities drive long-term dynamics. Numerical simulations reveal that over-reliance on custodial sentencing perpetuates recidivism and incarceration, while prioritising non-custodial disposals and rehabilitation reduces both ℛ 0 and CCR. Findings indicate that indiscriminate incarceration of petty offenders entrenches criminal cycles. Evidence-based interventions focused on rehabilitation and relapse prevention offer durable crime reduction. This quantitative framework evaluates justice policies, highlighting reforms that integrate deterrence with effective rehabilitation.