There is a growing interest in using mathematical models to understand crime dynamics, crime prevention, and detection. The past decade has experienced a relative reduction in conventional crimes, but this has been replaced by significant increases in cybercrime. We use a system of nonlinear differential equations to explore the impact of criminal location in relation to cyber networks on the amount of cybercrime. Using steady-state analysis and extensive numerical simulations, we find that the location of criminals relative to the network does not impact the system qualitatively although there are quantitative differences. Cyber networks that are more clustered are likely to experience greater levels of cybercrime but there is also a saturation effect that limits the level of victimisation as the number of criminals attempting to undertake crimes on a given network increases.

The interplay between criminal activity and crime control/prevention measures is inherently dynamic. This paper presents a simple nonlinear dynamical system in which criminal activity levels are coupled to policing effort. Through the process of non-dimensionalisation and sensitivity analysis, policing efficiency and the responsiveness of policing effort are identified as key parameter groupings. An analysis of the system shows that bi-stability is a feature of the dynamics. When there is no feedback between criminal activity and police recruitment, a saddle-node bifurcation occurs and threshold levels of criminal activity are required for the activity to be maintained. When feedback is permitted, we also find a backward bifurcation and criminal activity can be contained for policing efficiency below its threshold level. We demonstrate proof of concept for how the model might be used as a predictive tool with real data.