Contagious Criminal Career Models Showing Backward Bifurcations: Implications for Crime Control Policies

摘要

We provide a theoretical framework to study how criminal behaviors can be treated as an infectious phenomenon. There are two infectious diseases like models that mimic the role of convicted criminals in contaminating individuals not yet engaged in the criminal career. Equilibrium analyses of each model are studied in detail. The models proposed in this work include the social, economic, personal, and pressure from peers aspects that can, theoretically, determine the probability with which a susceptible individual with criminal propensity engages in a criminal career.These crime-inducing parameters are treatedmathematically and their inclusion in the model aims to help policy-makers design crime control strategies.We propose, to the best of our knowledge by the first time in quantitative criminology, the existence of thresholds for the stability of crime-endemic equilibriumwhich are the equivalent to the "basic reproduction number" widely used in themathematical epidemiology literature. Both models presented the phenomena of backward bifurcation and breaking-pointwhen the contact rates are chosen as bifurcation parameters.The finding of backward bifurcation in bothmodels implies that there is an endemic equilibriumof criminality evenwhen the threshold parameter for contagion is below unit, which, in turn, implies that control strategies are more difficult to achieve considerable impact on crime control.