Calculation of epidemic arrival time distributions using branching processes

Physical Review. E
Alastair Jamieson-Lane, Bernd Blasius

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.

References

Jan 1, 1986·Bulletin of Mathematical Biology·A J Coldman, J H Goldie
Oct 13, 2004·Proceedings of the National Academy of Sciences of the United States of America·L HufnagelT Geisel
Oct 13, 2007·Physical Review Letters·Vittoria Colizza, Alessandro Vespignani
Jan 29, 2008·Journal of Theoretical Biology·Aurélien GautreauMarc Barthélemy
Jan 21, 2010·Journal of the Royal Society, Interface·Pablo KaluzaBernd Blasius
Apr 25, 2013·Ecology Letters·H SeebensB Blasius
Dec 18, 2013·Science·Dirk Brockmann, Dirk Helbing
Feb 18, 2017·Physical Review. E·Flavio IannelliIgor M Sokolov
Feb 3, 2018·Chaos·Lawrence M ChenAnne Shapiro

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