Local Existence and Uniqueness of Solutions to a Pde Model for Criminal Behavior

The analysis of criminal behavior with mathematical tools is a fairly new idea, but one which can be used to obtain insight on the dynamics of crime. In a recent work 33 Short et al. developed an agent-based stochastic model for the dynamics of residential burglaries. This model produces the right qualitative behavior, that is, the existence of spatio-temporal collections of criminal activities or “hotspots,” which have been observed in residential burglary data. In this paper we prove local existence and uniqueness of solutions to the continuum version of this model, a coupled system of partial differential equations, as well a continuation argument. Furthermore, we compare this PDE model with a generalized version of the Keller-Segel model for chemotaxis as a first step to understanding possible conditions for global existence vs. blow-up of the solutions in finite time.