Statistical models of criminal behavior: the effects of law enforcement actions. (English) Zbl 1202.62177
Summary: We extend an agent-based model of crime-pattern formation initiated by M. B. Short et al. [Math. Models Methods Appl. Sci. 18, Suppl., 1249–1267 (2008; Zbl 1180.35530)] by incorporating the effects of law enforcement agents. We investigate the effect that these agents have on the spatial distribution and overall level of criminal activity in a simulated urban setting. Our focus is on a two-dimensional lattice model of residential burglaries, where each site (target) is characterized by a dynamic attractiveness to burglary and where criminal and law enforcement agents are represented by random walkers. The dynamics of the criminal agents and the target-attractiveness field are, with certain modifications, as described by Short et al. Here the dynamics of enforcement agents are affected by the attractiveness field via a biasing of the walk, the detailed rules of which define a deployment strategy. We observe that law enforcement agents, if properly deployed, will in fact reduce the total amount of crime, but their relative effectiveness depends on the number of agents deployed, the deployment strategy used, and spatial distribution of criminal activity. For certain policing strategies, continuum PDE models can be derived from the discrete systems. The continuum models are qualitatively similar to the discrete systems at large system sizes.
MSC:
| 62P25 | Applications of statistics to social sciences |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 65C20 | Probabilistic models, generic numerical methods in probability and statistics |
Citations:
Zbl 1180.35530Software:
ChemotaxisReferences:
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