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In the study of epidemic dynamics a fundamental question is whether apathogen initially affecting only one individual will give rise to a limitedoutbreak or to a widespread pandemic. The answer to this question cruciallydepends not only on the parameters describing the infection and recoveryprocesses but also on where, in the network of interactions, the infectionstarts from. We study the dependence on the location of the initial seed forthe Susceptible-Infected-Susceptible epidemic dynamics in continuous time onnetworks. We first derive analytical predictions for the dependence on theinitial node of three indicators of spreading influence (probability tooriginate 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 approachworks fairly well also on a set of real-world topologies of diverse nature. Weconclude by briefly investigating which topological network features determinedeviations from the theoretical predictions.

Influence of individual nodes for continuous-time Susceptible-Infected-Susceptible dynamics on synthetic and real-world networks