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
$r$
.