A statistical model of criminal behavior

Mathematical Models and Methods in Applied Sciences

Volumn 18, Issue SUPPL., 2008, Pages 1249-1267

  Short, M B ^a   D'Orsogna, M R ^b   Pasour, V B ^a   Tita, G E ^c   Brantingham, P J ^a   Bertozzi, A L ^a   Chayes, L B ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b CALIFORNIA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Crime models; Linear stability; Reaction diffusion equations

Indexed keywords

AGGLOMERATION; CHLORINE COMPOUNDS; CONTINUUM MECHANICS; DYNAMICS; LINEAR STABILITY ANALYSIS; OPTICAL BISTABILITY; TWO DIMENSIONAL;

CONTINUUM MODELING; CRIME MODELS; CRIMINAL ACTIVITIES; DISCRETE SYSTEMS; FEEDBACK MECHANISMS; HOT-SPOTS; LARGE SYSTEMS; LINEAR STABILITY; PARAMETER VALUES; QUANTITATIVE AGREEMENT; RANDOM WALKERS; REACTION-DIFFUSION EQUATIONS; SPATIO-TEMPORAL; STATISTICAL MODELLING; TWO-DIMENSIONAL LATTICE MODEL; URBAN SETTINGS;

LAW ENFORCEMENT;

EID: 49449089122     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202508003029     Document Type: Article

References (46)

1. L. Anselin, J. Cohen, D. Cook, W. Gorr and G. Tita, Criminal Justice 2000, Vol. 4 (National Institute of Justice, 2000), pp. 213-262.
2. D. Beavon, P. L. Brantingham and P. J. Brantingham, Crime Prevention Studies, Vol. 2 (Willow Tree Press, 1994), pp. 115-148.
3. N. Bellomo, A. Bellouquid, J. Nieto and J. J. Soler, Multicellular growing systems: Hyperbolic limits towards macroscopic description, Math. Mod. Meth. Appl. Sci. 17 (2007) 1675-1693.
4. M. Bendahmame, K. H. Karlsen and J. M. Urbano, On a two-sidely degenerate chemotaxis model with volume-filling effects, Math. Mod. Meth. Appl. Sci. 17 (2007) 783-804.
5. W. Bernasco and F. Luykx, Effects of attractiveness, opportunity and accessibility to burglars on residential burglary rates of urban neighborhoods, Criminology 41 (2003) 981-1001.
6. W. Bernasco and P. Nieuwbeerta, How do residential burglars select target areas? A new approach to the analysis of criminal location choice, Brit. J. Criminology 45 (2005) 296-315.
7. A. E. Bottoms and P. Wiles, Crime, Policing and Place: Essays in Environmental Criminology (Routledge, 1992), pp. 11-35.
8. J. P. Boyd, Chebyshev and Fourier Spectral Methods, 2nd edn. (Dover, 2001).
9. P. J. Brantingham and P. L. Brantingham, Patterns in Crime (Macmillan, 1984).
10. P. J. Brantingham and P. L. Brantingham, Environmental Criminology, 2nd edn. (Waveland Press, 1991), pp. 27-54.
11. P. J. Brantingham and P. L. Brantingham, Criminality of place: Crime generators and crime attractors, Euro. J. Criminal Policy Res. 3 (1995) 5-26.
12. M. Burger, M. Di Francesco and Y. Dolak-Struss, The Keller-Segel model for chemotaxis with prevention of overcrowding: Linear vs. nonlinear diffusion, SIAM J. Math. Anal. 38 (2006) 1288-1315.
13. H. M. Byrne and M. R. Owen, A new interpretation of the Keller-Segel model based on multiphase modelling, J. Math. Biol. 49 (2004) 604-626.
14. F. A. Chalub, Y. Dolak-Struss, P. Markowich, D. Oeltz, C. Schmeiser and A. Soref, Model hierarchies for cell aggregation by chemotaxis, Math. Mod. Meth. Appl. Sci. 16 (2006) 1173.
15. F. A. Chalub, P. A. Markovich, B. Perthame and C. Schmeiser, Kinetic models for chemotaxis and their drift-diffusion limits, Mon. Math. 142 (2004) 123.
16. M. C. Cross and P. C. Hohenberg, Pattern formation outside of equilibrium, Rev. Mod. Phys. 65 (1993) 851-1112.
17. M. del Pino and J. Wei, Collapsing steady states of the Keller-Segel system, Nonlinearity 19 (2006) 661-684.
18. Y. Dolak and C. Schmeiser, Kinetic models for chemotaxis: Hydrodynamic limits and spatio temporal mechanisms, J. Math. Biol. 51 (2005) 595-615.
19. R. Erban and H. G. Othmer, From individual to collective behaviour in chemotaxis, SIAM J. Appl. Math. 65 (2004) 361-391.
20. C. Escudero, The fractional Keller-Segel model, Nonlinearity 19 (2006) 2909-2918.
21. M. K. Felson, Crime and Nature (Sage Publications, 2006).
22. F. Filbet, P. Laurençot and B. Perthame, Derivation of hyperbolic models for chemosensitive movement, J. Math. Biol. 50 (2005) 189-207.
23. M. A. Herrero and J. J. L. Velazquez, Chemotactic collapse for the Keller-Segel model, J. Math. Biol. 35 (1996) 177-194.
24. 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. Quantitative Criminology 23 (2007) 201-219.
25. S. D. Johnson, K. Bowers and A. Hirschfield, New insights into the spatial and temporal distribution of repeat victimisation, Br. J. Criminology 37 (1997) 224-244.
26. S. D. Johnson and K. J. Bowers, The burglary as clue to the future: The beginnings of prospective hot-spotting, Eur. J. Criminology 1 (2004) 237-255.
27. S. D. Johnson and K. J. Bowers, Domestic burglary repeats and space-time clusters: The dimensions of risk, Eur. J. Criminology 2 (2005) 67-92.
28. E. F. Keller and L. A. Segel, Initiation of slime mold aggregation viewed as an instability, J. Theor. Biol. 26 (1970) 399-415.
29. M. A. Lewis, K. A. J. White and J. D. Murray, Analysis of a model for wolf territories, J. Math. Biol. 35 (1997) 749-774.
30. S. Luckhaus and Y. Sugiyama, Large time behavior of solutions in super-critical cases to degenerate Keller-Segel systems, Math. Model. Numer. Anal. 40 (2006) 597-621.
31. L. McLaughlin, S. D. Johnson, D. Birks, K. J. Bowers and K. Pease, Police perceptions of the long and short term spatial distribution of residential burglary, Int. J. Police Sci. Management 9 (2007) 99-111.
32. P. R. Moorcroft, M. A. Lewis and R. Crabtree, Mechanistic home range models predict patterns of coyote territories in yellowstone, Proc. Roy. Soc. London B 273 (2006) 1651-1659.
33. H. G. Othmer and T. Hillen, The diffusion limit of transport equations II: Chemotaxis equations, SIAM J. Appl. Math. 62 (2002) 1222-1250.
34. J. H. Ratcliffe, Crime mapping and the training needs of law enforcement, Eur. J. Criminal Policy Res. 10 (2004) 65-83.
35. G. F. Rengert, Crime, Policing and Place: Essays in Environmental Criminology (Routledge, 1992), pp. 109-117.
36. G. F. Rengert, A. R. Piquero and P. R. Jones, Distance decay reexamined, Criminology 37 (1999) 427-445.
37. D. Roncek and R. Bell, Bars, blocks and crime, J. Environ. Sys. 11 (1981) 35-47.
38. T. Senba, Type II blowup of solutions to a simplified Keller-Segel system in two-dimensional domains, Nonlinear Anal. Th. Meth. Appl. Int. Multidisciplinary J. Ser. A: Th. Meth. 66 (2007) 1817-1839.
39. A. Stevens, The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particles systems, SIAM J. Appl. Math. 61 (2002) 183-212.
40. Y. Sugiyama, Global existence in sub-critical cases and finite time blow-up in supercritical cases to degenerate Keller-Segel systems, Differential and Integral Equations. Int. J. Th. Appl. 19 (2006) 841-876.
41. G. Tita, J. Cohen and J. Engberg, An ecological study of the location of gang "set space," Social Problems 52 (2005) 272-299.
42. G. Tita and G. Ridgeway, The impact of gang formation on local patterns of crime, J. Res. Crime Delinquency 44 (2007) 208-237.
43. J. J. L. Velazquez, Well-posedness of a model of point dynamics for a limit of the Keller-Segel system, J. Diff. Eqs. 206 (2004) 315-352.
44. W. F. Walsh, Compstat: An analysis of an emerging police managerial paradigm, Policing 24 (2001) 347-362.
45. J. Q. Wilson and G. L. Kelling, Broken windows and police and neighborhood safety, Atlantic Mon. 249 (1982) 29-38.
46. R. Wright and S. Decker, Burglars on the Job (Northeastern Univ. Press, 1994).