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Studying models of cyber epidemics over arbitrary complex networks can deepenour understanding of cyber security from a whole-system perspective. In thispaper, we initiate the investigation of cyber epidemic models that accommodatethe {\em dependences} between the cyber attack events. Due to the notoriousdifficulty in dealing with such dependences, essentially all existing cyberepidemic models have assumed them away. Specifically, we introduce the idea ofCopulas into cyber epidemic models for accommodating the dependences betweenthe cyber attack events. We investigate the epidemic equilibrium thresholds aswell as the bounds for both equilibrium and non-equilibrium infectionprobabilities. We further characterize the side-effects of assuming away thedue dependences between the cyber attack events, by showing that the resultsthereof are unnecessarily restrictive or even incorrect.

Cyber Epidemic Models with Dependences