An efficient curing policy for epidemics on graphs

We provide a dynamic policy for the rapid containment of a contagion process modeled as an SIS epidemic on a bounded degree undirected graph with n nodes. We show that if the budget r of curing resources available at each time is Omega(W), where W is the CutWidth of the graph, and also of order Omega(log n), then the expected time until the extinction of the epidemic is of order O(n/r), which is within a constant factor from optimal, as well as sublinear in the number of nodes. Furthermore, if the CutWidth increases only sublinearly with n, a sublinear expected time to extinction is possible with a sublinearly increasing budget r.