Crime modeling with levy flights

SIAM Journal on Applied Mathematics

Volumn 73, Issue 4, 2013, Pages 1703-1720

  Chaturapruek, Sorathan ^a   Breslau, Jonah ^b   Yazdi, Aniel ^c   Kolokolnikov, Theodore ^d   McCalla, Scott G ^c  

^a HARVEY MUDD COLLEGE   (United States)

^b POMONA COLLEGE   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d DALHOUSIE UNIVERSITY   (Canada)

Author keywords

Crime modeling; Fractional Laplacian; Hotspots; Levy flights; Superdiffusion; Turing analysis

Indexed keywords

AUTONOMOUS AGENTS; BROWNIAN MOVEMENT; COMPUTATIONAL METHODS; CONTINUUM MECHANICS; FAST FOURIER TRANSFORMS; LAPLACE TRANSFORMS; MATHEMATICAL OPERATORS; NUMERICAL METHODS;

CRIME MODELS; FRACTIONAL LAPLACIAN; HOTSPOTS; LEVY FLIGHTS; SUPERDIFFUSION; TURING ANALYSIS;

CRIME;

EID: 84884947646     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/120895408     Document Type: Article

References (41)

1. D. Beavon, P. L. Brantingham, and P. J. Brantingham, Crime Prevention Studies, Vol. 2, Willow Tree Press, Monsey, NY, 1994.
2. W. Bernasco and P. Nieuwbeerta, How do residential burglars select target areas? A new approach to the analysis of criminal location choice, Br. J. Criminol., 45 (2005), pp. 296-315.
3. A. E. Bottoms and P. Wiles, Explanations of time and place, in Crime, Policing and Place: Essays in Environmental Criminology, Routledge, New York, 1992, pp. 11-35.
4. P. Brantingham and P. Brantingham, Criminality of place, Eur. J. Crim. Policy Res., 3 (1995), pp. 5-26.
5. P. J. Brantingham and P. L. Brantingham, Patterns in Crime, Macmillan, New York, 1984.
6. D. Brockmann, L. Hufnagel, and T. Geisel, The scaling laws of human travel, Nature, 439 (2006), pp. 462-465.
7. J. E. Eck, S. Chainey, J. G. Cameron, M. Leitner, and R. E. Wilson, Mapping Crime: Understanding Hot Spots, National Institute of Justice, Washington, DC, 2005.
8. G. Farrell and K. Pease, Repeat Victimization, Criminal Justice Press, Monsey, New York, 2001.
9. G. Farrell, C. Phillips, and K. Pease, Like taking candy: Why does repeat victimization occur?, Br. J. Criminol., 35 (1995), pp. 384-399.
10. M. K. Felson, Crime and Nature, Sage Publications, Thousand Oaks, CA, 2006.
11. M. C. Gonzalez, C. A. Hidalgo, and A. L. Barabasi, Understanding individual human mobility patterns, Nature, 453 (2008), pp. 779-782.
12. R. B. P. Hesseling, Using data on offender mobility in ecological research, J. Quant. Criminol., 8 (1992), pp. 95-112.
13. B. D. Hughes, M. F. Shlesinger, and E. W. Montroll, Random walks with self-similar clusters, Proc. Natl. Acad. Sci. USA, 78 (1981), pp. 3287-3291.
14. D. Iron, M. J. Ward, and J. Wei, The stability of spike solutions to the one-dimensional Gierer-Meinhardt model, Phys. D, 150 (2001), pp. 25-62.
15. A. James, M. J. Plank, and A. M. Edwards, Assessing Levy walks as models of animal foraging, J. R. Soc. Interface, 8 (2011), pp. 1233-1247.
16. S. D. Johnson, Repeat burglary victimisation: A tale of two theories, J. Exp. Criminol., 4 (2008), pp. 215-240.
17. S. D. Johnson, W. Bernasco, K. J. Bowers, H. Elffers, J. Ratcliffe, G. Rengert, and M. Townsley, Space-time patterns of risk: A cross national assessment of residential burglary victimization, J. Quant. Criminol., 23 (2007), pp. 201-219.
18. S. D. Johnson and K. J. Bowers, The stability of space-time clusters of burglary, Br. J. Criminol., 44 (2004), pp. 55-65.
19. S. D. Johnson, K. Bowers, and A. Hirschfield, New insights into the spatial and temporal distribution of repeat victimization, Br. J. Criminol., 37 (1997), pp. 224-241.
20. T. Kolokolnikov, M. Ward, and J. Wei, The Stability of Steady-State Hot-Spot Patterns for a Reaction-Diffusion Model of Urban Crime, preprint, arXiv:1201.3090v1 [nlin.PS], 2012.
21. Y. Nec, Spike-type solutions to one dimensional Gierer-Meinhardt model with Levy flights, Stud. Appl. Math., 129 (2012), pp. 272-299.
22. M. O'Leary, Modeling criminal distance decay, Cityscape, 13 (2011), pp. 161-198.
23. J. H. Ratcliffe and M. J. McCullagh, Hotbeds of crime and the search for spatial accuracy, Geogr. Syst., 1 (1999), pp. 385-398.
24. J. H. Ratcliffe and G. F. Rengert, Near-repeat patterns in Philadelphia shootings, Security J., 21 (2008), pp. 58-76.
25. G. F. Rengert, The journey to crime, in Crime, Policing and Place: Essays in Environmental Criminology, Routledge, New York, 1992, pp. 109-117.
26. I. Rhee, M. Shin, S. Hong, K. Lee, S. J. Kim, and S. Chong, On the Levy-walk nature of human mobility, IEEE/ACM Trans. Netw., 19 (2011), pp. 630-643.
27. D. W. Roncek and R. Bell, Bars, blocks, and crimes, J. Environ. Syst., 11 (1981), pp. 35-47.
28. A. Sagovsky and S. D. Johnson, When does repeat burglary victimisation occur?, Aust. N. Z. J. Criminol., 40 (2007), pp. 1-26.
29. P. Santtila, M. Laukkanen, A. Zappal, and D. Bosco, Distance travelled and offence characteristics in homicide, rape, and robbery against business, Legal Criminol. Psych., 13 (2008), pp. 345-356.
30. M. B. Short, A. L. Bertozzi, and P. J. Brantingham, Nonlinear patterns in urban crime: Hotspots, bifurcations, and suppression, SIAM J. Appl. Dyn. Syst., 9 (2010), pp. 462-483.
31. M. B. Short, P. J. Brantingham, A. L. Bertozzi, and G. E. Tita, Dissipation and displacement of hotspots in reaction-diffusion models of crime, Proc. Natl. Acad. Sci. USA, 107 (2010), pp. 3961-3965.
32. M. B. Short, M. D'Orsogna, P. J. Brantingham, and G. E. Tita, Measuring and modeling repeat and near-repeat burglary effects, J. Quant. Criminol., 25 (2009), pp. 325-339.
33. 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), pp. 1249-1267.
34. B. Snook, Individual differences in distance travelled by serial burglars, J. Investig. Psych. Offender Profil., 1 (2004), pp. 53-66.
35. M. Townsley, R. Homel, and J. Chaseling, Infectious burglaries. A test of the near repeat hypothesis, Br. J. Criminol., 43 (2003), pp. 615-633.
36. A. Tseloni and K. Pease, Repeat personal victimization. 'Boosts' or 'flags'?, Br. J. Criminol., 43 (2003), pp. 196-212.
37. A. Tseloni and K. Pease, Repeat personal victimization: Random effects, event dependence and unexplained heterogeneity, Br. J. Criminol., 44 (2004), pp. 931-945.
38. P. J. Van Koppen and R. W. J. Jansen, The road to the robbery: Travel patterns in commercial robberies, Br. J. Criminol., 38 (1998), pp. 230-246.
39. J. Q. Wilson and G. L. Kelling, Broken windows and police and neighborhood safety, Atlantic Mon., 249 (1982), pp. 29-38.
40. R. Wright and S. Decker, Burglars on the Job, Northeastern University Press, Boston, 1994.
41. A. Zoia, A. Rosso, and M. Kardar, Fractional Laplacian in bounded domains, Phys. Rev. E, 76 (2007), 021116.