A mathematical model of serious and minor criminal activity

Andrew Alfred Lacey, Michail Tsardakas

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)
161 Downloads (Pure)


Using mathematical methods to understand and model crime is a recent idea that has drawn considerable attention from researchers during the last five years. From the plethora of models that have been proposed, perhaps the most successful one has been a diffusion-type differential equations model that describes how the number of criminals evolves in a specific area. Wepropose a more detailed form of this model that allows for two distinct criminal types associated with major and minor crime. Additionally, we examine a stochastic variant of the model that represents more realistically the ‘generation’ of new criminals. Numerical solutions from both models are presented and compared with actual crime data for the Greater Manchesterarea. Agreement between simulations and actual data is satisfactory. A preliminary statistical analysis of the data also supports the model’s potential to describe crime.
Original languageEnglish
Pages (from-to)403-421
Number of pages19
JournalEuropean Journal of Applied Mathematics
Issue number3
Early online date8 Apr 2016
Publication statusPublished - Jun 2016


  • Crime
  • Differential equations
  • Mathematical model


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