  The rise of the World Airline Network over the past century has lead to sharp
changes in our notions of `distance' and `closeness' - both in terms of trade
and travel, but also (less desirably) with respect to the spread of disease.
When novel pathogens are discovered, countries, cities and hospitals are caught
trying to predict how much time they have to prepare. In this paper, by
considering the early stages of epidemic spread as a simple branching process,
we derive the full probability distribution of arrival times. We are able to
re-derive a number of past arrival time results (in suitable limits), and
demonstrate the robustness of our approach, both to parameter values far
outside the traditionally considered regime, and to errors in the parameter
values used. The branching process approach provides some theoretical
justification to the `effective distance' introduced by Brockmann & Helbing
(2013), however we also observe that when compared to real world data, the
predictive power of all methods in this class is significantly lower than has
been previously reported.
