Department of Mathematics Colloquium


Abstract 

Disease breaks out on a graph! As medicine is
expensive, it is unrealistic to send medicine to all vertices in
preparation to fight the outbreak, but we still desire to ensure that
the disease dies out quickly on the medicated vertices and escapes the
medicated set with low probability. Under a variant of the contact
process, a classical model of the spread of disease, we show how to
accomplish such a goal on an arbitrary host graph. In particular, we show that the probability that the disease escapes a given medicated set can be bounded in terms of the PageRank of the complement. We additionally look at a broad generalization of this, where multiple interacting processes spread on a graph, where a new vectorized version of PageRank becomes critical to our understanding of the process.
