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
