Criminals and their models - a review of epidemiological models describing criminal behaviour
Joanna Sooknanan, Terence Seemungal
Abstract
Mathematical models are increasingly being adapted to model criminal behaviour and may be used to support traditional crime prevention methods. This review focuses on recent efforts to model criminal behaviour associated with gangs, delinquency, terrorism and corruption via modified infectious disease compartmental models. Similar to their disease counterparts, models are based on the premise that these behaviours are contagious, spread through association/contact with delinquent peers. Models are classified by the functions used to describe contact rates, by their use of optimal control techniques and by their country of origin. An examination of the functions used to describe contact rates showed that the majority of these models used either a mass action or a standard incidence contact rate, with mass action being more prevalent. Models that incorporated optimal control techniques, specifically utilized Pontryagin's maximum principle with a quadratic control on the objective function to determine mitigation strategies. The most effective strategy was generally found to be an early prevention approach through education and awareness. When models were distinguished by their country of origin, it was observed that most of the models were formulated for, or in, developing nations. In addition to reviewing models, challenges involved in the modelling process are highlighted.