Efficient control of epidemics over random networks

Motivated by the modeling of the spread of viruses or epidemics with coordination among agents, we introduce a new model generalizing both the basic contact model and the bootstrap percolation. We analyze this percolated threshold model when the underlying network is a random graph with fixed degree distribution. Our main results unify many results in the random graphs literature. In particular, we provide a necessary and sufficient condition under which a single node can trigger a large cascade. Then we quantify the possible impact of an attacker against a degree based vaccination and an acquaintance vaccination. We define a security metric allowing to compare the different vaccinations. The acquaintance vaccination requires no knowledge of the node degrees or any other global information and is shown to be much more efficient than the uniform vaccination in all cases.