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Crime Modeling with Truncated Levy Flights and Effects of Police Patrol | | Chaohao Pan
; Bo Li
; Yuqi Zhang
; Nathan Geldner
; Chuntian Wang
; Li Wang
; Andrea Bertozzi
; | | Date: |
1 Jan 2016 | | Abstract: | In this paper, we developed a truncated Levy flight model to study the crime
dynamics. In the discrete case, our model allows criminals to perform long
jumps in between committing crimes with a speed light. This is a more realistic
extension of a pioneering random walk model by Short et. al and a Levy flight
model thereafter in Chaturapruek, et al. We also derive a continuum limit and
perform a stability analysis to study the formation of crime hotspots. Our
model is more realistic than the Levy Flight Model, and provides an alternative
to the Random Walk Model when the criminals can perform long jumps in between
committing crimes. In the next step, we introduce patrolling police officers to
our new model following that in. We examine the effects of police patrol when
the police choose to adopt different strategies, including unbiased random
walk, biased random walk, and truncated Levy flight. We evaluate the
effectiveness of the police patrol with the number of crime events in a given
time frame. With spatially non-uniform initial conditions, we find that the
truncated Levy flight to be the best strategy in general. | | Source: | arXiv, 1601.3415 | | Services: | Forum | Review | PDF | Favorites | |
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