  Statistical agent-based models for crime have shown that repeat victimization
can lead to predictable crime hotspots (see e.g. Short et al., Math. Models
Methods Appl., 2008), then a recent study in one space dimension (Chaturapruek
et al., SIAM J. Appl. Math, 2013) shows that the hotspot dynamics changes when
movement patterns of the criminals involve long-tailed L\'evy distributions for
the jump length as opposed to classical random walks. In reality, criminals
move in confined areas with a maximum jump length. In this paper we develop a
mean-field continuum model with truncated L\'evy flights for residential
burglary in one space dimension. The continuum model yields local Laplace
diffusion, rather than fractional diffusion. We present an asymptotic theory to
derive the continuum equations and show excellent agreement between the
continuum model and the agent-based simulations. This suggests that local
diffusion models are universal for continuum limits of this problem, the
important quantity being the diffusion coefficient. Law enforcement agents are
also incorporated into the model, and the relative effectiveness of their
deployment strategies are compared quantitatively.
