A Note on Dependence of Epidemic Threshold on State Transition Diagram in the SEIC Cybersecurity Dynamical System Model

摘要

Cybersecurity dynamical system model is a promising tool to describe and understand virus spreading in networks. The modelling comprises of two issues: the state transition diagram and the infection graph. Most works focus on proposing models (the state transition diagram) and studying the relationship between dynamics and the infection graph topology. In this paper, We propose the SEIC model and illustrate how the model transition diagram influence the dynamics, in particular, the epidemic threshold by calculating and comparing their thresholds in a class of Secure-Exposed-Infectious-Cured (SEIC) models. We show that as a new state enters the state transition diagram in the fashion of the SEIC model, the epidemic threshold increases, which implies that the model has a larger region of parameters to be stabilized. Numerical examples are presented to verify the theoretical results.