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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 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 nonequilibrium 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.

Modeling and analyzing security of networked systems is an important problem in the emerging Science of Security and has been under active investigation. In this paper, we propose a new approach towards tackling the problem. Our approach is inspired by the shock model and random environment techniques in the Theory of Reliability, while accommodating security ingredients. To the best of our knowledge, our model is the first that can accommodate a certain degree of adaptiveness of attacks, which substantially weakens the often-made independence and exponential attack inter-arrival time assumptions. The approach leads to a stochastic process model with two security metrics, and we attain some analytic results in terms of the security metrics.

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