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Toby Davies

Research subject

Thesis title: Complex Systems Approaches to Issues in Crime and Security

Primary supervisor: Professor Steven Bishop
Secondary supervisor: Dr Shane Johnson
Starting date: September, 2010
Projected completion date: September, 2013

My research concerns the mathematical modelling and analysis of issues related to security and crime. Such issues involve many factors, interacting in non-trivial ways, and as such are well-suited to treatment as complex systems and the use of associated tools. By attempting to model these factors, often using insight from quantitative social science, and their interactions, my aim is to provide a more thorough and well-rounded understanding of the mechanisms underlying security issues. This is done using techniques such as agent-based modelling and game theory, alongside more traditional differential-equation-based modelling. I am also particularly interested in applications of complex network theory to this area, where techniques originating in graph theory can be used.

Specifically, my current research is focussed on modelling spatio-temporal patterns of crime at the urban level, with specific focus on how this is influenced by the urban backcloth and layout of cities. A simulation-based approach is used to explore various criminological theories and mechanisms and to analyse the effect of changes to the backcloth or direct interventions.

My interest in complex networks also extends to social network analysis, and I hope to do some work modelling the interactions of terrorist groups or those engaged in organised crime.

I am also associated with the ENFOLDing project on the modelling of global dynamics, contributing to the Security workstream.


I completed my undergraduate study in Mathematics at Worcester College, University of Oxford in 2008, gaining an MMath. Since then, I have been a member of the SECReT Doctoral Training Centre at UCL, which is an EPSRC-funded programme in Security and Crime Science. As part of this, I was awarded an MRes in 2010, and am now working towards a PhD within the Mathematics department.

Publications and other work

Davies, T. P., Fry, H. M., Wilson, A. G., and Bishop, S. R. (2013) A mathematical model of the London riots and their policing, Nature Scientific Reports 3, Article number: 1303 doi:10.1038/srep01303