  Consider a random graph, having a pre-specified degree distribution F but
other than that being uniformly distributed, describing the social structure
(friendship) in a large community. Suppose one individual in the community is
externally infected by an infectious disease and that the disease has its
course by assuming that infected individuals infect their not yet infected
friends independently with probability p. For this situation the paper
determines R_0 and tau_0, the basic reproduction number and the asymptotic
final size in case of a major outbreak. Further, the paper looks at some
different local vaccination strategies where individuals are chosen randomly
and vaccinated, or friends of the selected individuals are vaccinated, prior to
the introduction of the disease. For the studied vaccination strategies the
paper determines R_v: the reproduction number, and tau_v: the asymptotic final
proportion infected in case of a major outbreak, after vaccinating a fraction
v.
