We give an analysis of a variant of the contact process on finite graphs, allowing for
nonuniform cure rates, modeling antidote
distribution. We examine an inoculation scheme using PageRank vectors
that 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 $1-2\ep$, 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 probabilistic
error bound $\ep$ and the infection rate, and the size of
$H$ depends only on $s$, $\ep$, and the topology around
the initially infected nodes, independent of the size of
the whole graph.