Abstract
The rise of the World Airline Network over the past century has led to sharp changes in our notions of "distance" and "closeness"-in terms of both 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 rederive 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 and Helbing [Science 342, 1337 (2013)SCIEAS0036-807510.1126/science.1245200]; 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.
Highlights
It was said by Jules Verne in 1873 that “The world has grown smaller, since a man can go round it ten times more quickly than a hundred years ago,” that one could travel around the world in 80 days [1]
Similar results are observed for scale-free networks. We find that both BP AT and effective distance arrival time (“ED AT”) methods give qualitatively similar results, and that these results would appear in many cases plausible: for example, in the case of Severe Acute Respiratory Syndrome (SARS), we observe that predicted arrival times in both South Korea and Hong Kong are low, while the arrival time in the United States
Better understanding the spread of epidemics through the World Aviation Network (WAN) allows for both real-time forecasting and the possibility of network design, making changes to the WAN or local transport networks so as to slow epidemic spread [8]
Summary
It was said by Jules Verne in 1873 that “The world has grown smaller, since a man can go round it ten times more quickly than a hundred years ago,” that one could travel around the world in 80 days [1]. Depending on the questions being asked, explicit modeling of such intricate details may be necessary; for other questions, such as the determination of epidemic arrival time (AT), it seems that simpler methods may suffice For this reason, a number of authors [12,13,14,15] have proposed a variety of heuristics and metrics—artificial measures of distance based on flight data from the WAN. Where our predictions disagree with observed arrival times for realworld epidemics, this is suggestive of either flaws in the data, or gaps in the underlying model, gaps that will require not better mathematics, but instead better understanding of the system under study
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