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

Abstract

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 treated mathematically 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 equilibrium which are the equivalent to the "basic reproduction number" widely used in the mathematical epidemiology literature. Both models presented the phenomena of backward bifurcation and breaking-point when the contact rates are chosen as bifurcation parameters. The finding of backward bifurcation in both models implies that there is an endemic equilibrium of criminality even when 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.

A model-based assessment of the cost-benefit balance and the plea bargain in criminality -- A qualitative case study of the Covid-19 epidemic shedding light on the "car wash operation" in Brazil

“…Raimundo et al [15] described the criminal contagion from inside Brazil's prison system to outside susceptible individuals with criminal propensity. In the model, they assumed that the behavioral contagion rate was proportional to the product between the numbers of crime-susceptible and incarcerated individuals, which is known in the disease epidemics modelings as mass action law [2].…”

A minimal model coupling communicable and non-communicable diseases

“…On the other hand, external dynamics may impoverish/take out of poverty people, which is also a risk factor in front of a CD. Note that the transmission of the NCD could still be formulated considering more sophisti-cated functional terms [23], [21], but we disregard this approach here to keep the model formulation minimal as mentioned. The dynamics of the transmissible disease is somehow similar to (but not exactly) the classical SIS model [2] with density-dependent transmission.…”