Quantitative models in crime control

In this study we propose several mathematical models for describing the behavior of crime-related systems. In the first part is presented a simple model for describing and measuring crime systems with recidivism. This model may be used in estimating the quantitative effects of alternative policies on crime rates. An important factor not recognized by the model is deterrence. One derivative of the mathematical analyses is a proposed method for measuring the relative severity of sentencing in a given system. The second part of the paper deals with the criminal population as a whole, trying to bring into account the non-stationary behavior of the system. This study should be regarded as a preliminary attempt to develop elementary mathematical models fitting crime systems. Some of the assumptions do not have substantial direct support by data.