  In the study of epidemic dynamics a fundamental question is whether a
pathogen initially affecting only one individual will give rise to a limited
outbreak or to a widespread pandemic. The answer to this question crucially
depends not only on the parameters describing the infection and recovery
processes but also on where, in the network of interactions, the infection
starts from. We study the dependence on the location of the initial seed for
the Susceptible-Infected-Susceptible epidemic dynamics in continuous time on
networks. We first derive analytical predictions for the dependence on the
initial node of three indicators of spreading influence (probability to
originate an infinite outbreak, average duration and size of finite outbreaks)
and compare them with numerical simulations on random uncorrelated networks,
finding a very good agreement. We then show that the same theoretical approach
works fairly well also on a set of real-world topologies of diverse nature. We
conclude by briefly investigating which topological network features determine
deviations from the theoretical predictions.
