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Mathematics > Probability

arXiv:1401.0914 (math)
[Submitted on 5 Jan 2014]

Title:The front of the epidemic spread and first passage percolation

Authors:Shankar Bhamidi, Remco van der Hofstad, Julia Komjathy
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Abstract:In this paper we establish a connection between epidemic models on random networks with general infection times considered in Barbour and Reinert 2013 and first passage percolation. Using techniques developed in Bhamidi, van der Hofstad, Hooghiemstra 2012, when each vertex has infinite contagious periods, we extend results on the epidemic curve in Barbour Reinert 2013 from bounded degree graphs to general sparse random graphs with degrees having finite third moments as the number of vertices tends to infinity. We also study the epidemic trail between the source and typical vertices in the graph. This connection to first passage percolation can be also be used to study epidemic models with general contagious periods as in Barbour Reinert 2013 without bounded degree assumptions.
Comments: 14 pages
Subjects: Probability (math.PR)
Cite as: arXiv:1401.0914 [math.PR]
  (or arXiv:1401.0914v1 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1401.0914
Journal reference: Journal of Applied Probability Volume 51A (2014), 101-121
Related DOI: https://doi.org/10.1239/jap/1417528470

Submission history

From: Julia Komjathy [view email]
[v1] Sun, 5 Jan 2014 17:27:52 UTC (57 KB)
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