  A Reed-Frost epidemic with inhomogeneous infection probabilities on a graph
with prescribed degree distribution is studied. Each edge $(u,v)$ in the graph
is equipped with two weights $W_{(u,v)}$ and $W_{(v,u)}$ that represent the
(subjective) strength of the connection and determine the probability that $u$
infects $v$ in case $u$ is infected and vice versa. Expressions for the
epidemic threshold are derived for i.i.d.\ weights and for weights that are
functions of the degrees. For i.i.d.\ weights, a variation of the so called
acquaintance vaccination strategy is analyzed where vertices are chosen
randomly and neighbors of these vertices with large edge weights are
vaccinated. This strategy is shown to outperform the strategy where the
neighbors are chosen randomly in the sense that the basic reproduction number
is smaller for a given vaccination coverage.
