Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

A mathematical model of a criminal-prone society

Pages: 193 - 207, Volume 4, Issue 1, February 2011      doi:10.3934/dcdss.2011.4.193

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Juan Carlos Nuño - Departamento de Matemática Aplicada a los Recursos Naturales, E.T.S.I. Montes. Universidad Politécnica de Madrid, 28040 Madrid, Spain (email)
Miguel Angel Herrero - IMI and Departamento de Matemática Aplicada. Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain (email)
Mario Primicerio - Dipartimento di Matematica, università degli Studi di Firenze, 55015 Firenze, Italy (email)

Abstract: Criminals are common to all societies. To fight against them the community takes different security measures as, for example, to bring about a police. Thus, crime causes a depletion of the common wealth not only by criminal acts but also because the cost of hiring a police force. In this paper, we present a mathematical model of a criminal-prone self-protected society that is divided into socio-economical classes. We study the effect of a non-null crime rate on a free-of-criminals society which is taken as a reference system. As a consequence, we define a criminal-prone society as one whose free-of-criminals steady state is unstable under small perturbations of a certain socio-economical context. Finally, we compare two alternative strategies to control crime: (i) enhancing police efficiency, either by enlarging its size or by updating its technology, against (ii) either reducing criminal appealing or promoting social classes at risk.

Keywords:  Criminality, population dynamics, nonlinear dynamical system, social mobility.
Mathematics Subject Classification:  Primary: 91D10, 34A34; Secondary: 37N40.

Received: November 2008;      Revised: April 2009;      Available Online: October 2010.