Spread of epidemic-like failures in telecommunication networks

We study epidemic-like failures in telecommunication networks. A mean-field model taking two levels of failure into account is introduced where infection, recovery and transition rates are node/link specific. Regarding the short-term epidemic outbreak, an epidemic threshold is stated in terms of the basic reproduction number computed as the largest eigenvalue of a weighted adjacency matrix of the network. As to the long-term endemic situation, we have proved the existence and uniqueness of a steady state. We check the accuracy of the model by means of Monte Carlo simulations. To improve the level of accuracy, we propose a slight modification of the mean-field equations which changes the way we compute the probability for a node of acquiring the infection from one of its neighbors. As a consequence, correlations between probabilities of different states are implicitly incorporated into the model giving improved predictions and being very close to simulation-based data.