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Phys Rev E. 2017 Jan;95(1-1):012313. doi: 10.1103/PhysRevE.95.012313. Epub 2017 Jan 17.

Effective distances for epidemics spreading on complex networks.

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Institute for Physics, Humboldt-University of Berlin, Newtonstraße 15, 12489 Berlin, Germany.
Institute for Theoretical Physics, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.
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.


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.

[Indexed for MEDLINE]

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