Mathematical modelling of criminal activity

Abstract

Using mathematical methods to understand and model crime is a recent idea that has drawn considerable attention from researchers during the last fifteen years. From the plethora of models that have been proposed, perhaps the most successful one has been a diffusion-type partial differential equations model that describes how the number of criminals evolves in a specific area. We propose a number of versions of this model that allow for two distinct criminal types associated with serious and minor crime. Additionally, we examine stochastic variants of the model and present numerical solutions. Our model’s assumptions are supported by analysing spatiotemporal data of criminal activity in England and the USA.