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2018 Contagious Criminal Career Models Showing Backward Bifurcations: Implications for Crime Control Policies
Silvia Martorano Raimundo, Hyun Mo Yang, Eduardo Massad
J. Appl. Math. 2018: 1-16 (2018). DOI: 10.1155/2018/1582159

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.

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Silvia Martorano Raimundo. Hyun Mo Yang. Eduardo Massad. "Contagious Criminal Career Models Showing Backward Bifurcations: Implications for Crime Control Policies." J. Appl. Math. 2018 1 - 16, 2018. https://doi.org/10.1155/2018/1582159

Information

Received: 7 March 2018; Revised: 30 May 2018; Accepted: 3 July 2018; Published: 2018
First available in Project Euclid: 19 September 2018

zbMATH: 07000932
MathSciNet: MR3842718
Digital Object Identifier: 10.1155/2018/1582159

Rights: Copyright © 2018 Hindawi

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