title: Effective distances for epidemics spreading on complex networks.
abstract: We show that the recently introduced logarithmic metrics used to predict disease arrival times on complex networks are approximations of more general network-based measures derived from random walks theory. Using the daily air-traffic transportation data we perform numerical experiments to compare the infection arrival time with this alternative metric that is obtained by accounting for multiple walks instead of only the most probable path. The comparison with direct simulations reveals a higher correlation compared to the shortest-path approach used previously. In addition our method allows to connect fundamental observables in epidemic spreading with the cumulant-generating function of the hitting time for a Markov chain. Our results provides a general and computationally efficient approach using only algebraic methods.
authors.affiliation: Institute for Physics, Humboldt-University of Berlin, Newtonstraße 15, 12489 Berlin, Germany.
authors.forename: Flavio
authors.initials: F
authors.lastname: Iannelli
authors.affiliation: Institute for Theoretical Physics, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.
authors.forename: Andreas
authors.initials: A
authors.lastname: Koher
authors.affiliation: Robert Koch-Institute, Nordufer 20, 13353 Berlin, Germany.|Institute for Theoretical Biology and Integrative Research Institute of Life Sciences, Humboldt-University of Berlin, Philippstraße 13, Haus 4, 10115 Berlin, Germany.
authors.forename: Dirk
authors.initials: D
authors.lastname: Brockmann
authors.affiliation: Institute for Theoretical Physics, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.
authors.forename: Philipp
authors.initials: P
authors.lastname: Hövel
authors.affiliation: Institute for Physics, Humboldt-University of Berlin, Newtonstraße 15, 12489 Berlin, Germany.
authors.forename: Igor M
authors.initials: IM
authors.lastname: Sokolov
mesh_terms: D064870:Air Travel; D059028:Airports; D003198:Computer Simulation; D058872:Epidemics; D006801:Humans; D038622:Internationality; D008390:Markov Chains; D008954:Models, Biological; D013997:Time Factors