Which nodes are most vulnerable to an epidemic spreading through a
network, and which carry the highest risk of causing a major outbreak if
they are the source of the infection? In this talk I will show how these
questions can be answered to good approximation using the cavity method.
Several curious properties of node vulnerability and risk are explored:
some nodes are more vulnerable than others to weaker infections, yet
less vulnerable to stronger ones; a node is always more likely to be
caught in an outbreak than it is to start one, except when the disease
has a deterministic lifetime; the rank order of node risk depends on the
details of the distribution of infectious periods.