  We study metapopulation models for the spread of epidemics in which different
subpopulations (cities) are connected by fluxes of individuals (travelers).
This framework allows to describe the spread of a disease on a large scale and
we focus here on the computation of the arrival time of a disease as a function
of the properties of the seed of the epidemics and of the characteristics of
the network connecting the various subpopulations. Using analytical and
numerical arguments, we introduce an easily computable quantity which
approximates this average arrival time. We show on the example of a disease
spread on the world-wide airport network that this quantity predicts with a
good accuracy the order of arrival of the disease in the various subpopulations
in each realization of epidemic scenario, and not only for an average over
realizations. Finally, this quantity might be useful in the identification of
the dominant paths of the disease spread.
