Exploring the impact of how criminals interact with cyber-networks—a mathematical modeling approach

ABSTRACT

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 The past decade has experienced a relative reduction in conventional crimes, but this has been replaced by significant increases in cybercrime. In this paper, we use deterministic modelling to describe the spread of cybercrime across a cyber-network by describing the heterogeneity of interactions between individuals using a nonlinear interaction between individuals in the network, and we allow criminals to operate either internally or externally to the cyber-network. We are able to determine the impact of the location of the criminal relative to the cyber-network which is being attacked. The model structure incorporates key elements of a social network structure thereby allowing for limited rates of victimisation. Both model structure and our observations are novel and provide a new contribution to the theoretical discussion of cybercrime dynamics, offering potential avenues to consider control strategies. 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 given network increases. We discuss model limitations and describe how the model might be used with datasets to translate the theoretical findings into a useful tool in the fight to detect and eradicate cybercrime activity.

KEYWORDS:

• mathematical model
• cybercrime
• victims
• criminals
• steady-state analysis

Acknowledgements

This work was undertaken within the UK-Africa Postgraduate Advanced Study Institute in Mathematical Sciences funded by UKRI Global Challenges Research Fund, grant number EP/T00410X/1.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/27684830.2023.2295059.

Additional information

Funding

The work was supported by the UK Research and Innovation [EP/T00410X/1].