  Studying models of cyber epidemics over arbitrary complex networks can deepen
our understanding of cyber security from a whole-system perspective. In this
paper, we initiate the investigation of cyber epidemic models that accommodate
the {\em dependences} between the cyber attack events. Due to the notorious
difficulty in dealing with such dependences, essentially all existing cyber
epidemic models have assumed them away. Specifically, we introduce the idea of
Copulas into cyber epidemic models for accommodating the dependences between
the cyber attack events. We investigate the epidemic equilibrium thresholds as
well as the bounds for both equilibrium and non-equilibrium infection
probabilities. We further characterize the side-effects of assuming away the
due dependences between the cyber attack events, by showing that the results
thereof are unnecessarily restrictive or even incorrect.
