Distributing Antidote Using PageRank Vectors

We give an analysis of a variant of the contact process on finite graphs, allowing for non-uniform cure rates, modeling antidote distribution. We examine an inoculation scheme using PageRank vectors which quantify the correlations among vertices in the contact graph. We show that for a contact graph on n nodes we can select a set H of nodes to inoculate such that with probability at least 1−2 , any infection from any starting infected set of s nodes will die out in c log s+ c′ time, where c and c′ depend only on the probabilitstic error bound and the infection rate, and the size of H depends only on s, and the topology around the initially infected nodes, independent of the size of the whole graph.