Project B7 (finished)

Project B 7 - Jens Struckmeier, Stefan Heitmann: Space-Time pattern of criminal activity

Principal investigator: Jens Struckmeier

Background and Motivation

In criminology literature it is a well-documented feature that criminal activity shows up in persistent areas of high concentration (hot spots). Mathematical modelling of criminal activity aims to study the formation and dynamics of those patterns.

One approach is purely data-driven based on detailed empirical data thas has become available during the last decade. Space-time interaction tests that have been borrowed from epidemicity and demography are applied to extract typical time and length scales on which patterns of increased criminal activity take place.

The second approach aims to identify the mechanism that are responsible for the observed pattern formation. It borrows systems of partial differential equations from theoretical biology and theoretical neuroscience . Those systems usually comprise reaction-diffusion equations for the variables 'criminal activity concentrations' and  'propensity of locations to become subject of crime'  

The work is a joint project with the Hamburg and the Lower Saxony State Offices of Criminal Investigation.

Aims and Objectives

The first approach has been succesfully applied to burglary data from 2012. The space-time interaction criterion introduced by Knox (1963) reveals typical pattern of incidence.

The currently chosen starting point for the second approach is based on a reaction-diffusion system that resembles the classical Keller-Segel model. The Keller-Segel sytem of equations describes the movement of an organism in response to a chemical stimulus. In theoretical biology, this behaviour is denoted chemotaxis.

In application to criminal activity, our main focus is on the role of boundary conditions. Those can  - different from the situation in biology - not be specified with reasonable accuracy.

Student:Two Master Thesises in 2016 and 2017 have been completed within this project.

Publications

Aleander Gluba, Stefan Heitmann and Nina Hermes, Reviktimisierung bei Wohnungseinbrüchen, Seite 368-376, KRIMINALISTIK 6, 2015.