CoMSES Catalog

Crime modeling with truncated Levy flights for residential burglary models

Authored by Andrea L Bertozzi, Chaohao Pan, Bo Li, Chuntian Wang, Yuqi Zhang, Nathan Geldner, Li Wang

Date Published: 2018

DOI: 10.1142/s0218202518400080

Sponsors: United States National Science Foundation (NSF)

Platforms: No platforms listed

Model Documentation: Other Narrative Flow charts Mathematical description

Model Code URLs: Model code not found

Abstract

Statistical agent-based models for crime have shown that repeat victimization can lead to predictable crime hotspots (see e.g. M. B. Short, M. R. D'Orsogna, V. B. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi and L. B. Chayes, A statistical model of criminal behavior, Math. Models Methods Appl. Sci. 18 (2008) 1249-1267.), then a recent study in one-space dimension (S. Chaturapruek, J. Breslau, D. Yazdi, T. Kolokolnikov and S. G. McCalla, Crime modeling with Levy flights, SIAM J. Appl. Math. 73 (2013) 1703-1720.) shows that the hotspot dynamics changes when movement patterns of the criminals involve long-tailed Levy 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 Levy flights (TLFs) 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.

Crime modeling with truncated Levy flights for residential burglary models

Abstract

Tags