Epidemic model for malware targeting telephony networks

In this paper, we present a new mathematical epidemiological model of a malware targeting Private Branch eXchanges (PBX). Although the term PBX is old, we argue that traditional PBXs are still extensively used, along the modern VoIP systems, forming part of most nations' critical infrastructure. The proposed model is based on graph theory and generic epidemiological models. Through this model we are able to simulate infections of PBX malware and monitor their evolution. We provide estimations of potential scale and timing characteristics of virus propagation over the PBX network with a mathematical framework to model PBX malware, an epidemic model for PBX infections and an empirical study of the model under a simplified environment. Our results show that 2 days are sufficient for the malware diffusion, highlighting the necessity of immediate countermeasures.