Juan Carlos Nuño - Departamento de Matemática Aplicada a los Recursos Naturales, E.T.S.I. Montes. Universidad Politécnica de Madrid, 28040 Madrid, Spain (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,
Received: November 2008; Revised: April 2009; Published: October 2010.