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The front of the epidemic spread and first passage percolation

Part of: Operations research and management science Graph theory Combinatorial probability

Published online by Cambridge University Press:  30 March 2016

Shankar Bhamidi ,
Remco van der Hofstad  and
Júlia Komjáthy
Shankar Bhamidi
Affiliation:
Department of Statistics, University of North Carolina, Chapel Hill, USA. Email address: [email protected].
Remco van der Hofstad
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands. Email address: [email protected].
Júlia Komjáthy
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands. Email address: [email protected].
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Abstract

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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 and Hooghiemstra (2012), when each vertex has infinite contagious periods, we extend results on the epidemic curve in Barbour and Reinert (2013) from bounded degree graphs to general sparse random graphs with degrees having finite second moments as n → ∞, with an appropriate X2log+X condition. We also study the epidemic trail between the source and typical vertices in the graph.

Keywords

Flowrandom graphrandom networkepidemics on random graphsfirst passage percolationhop countinteracting particle system

MSC classification

Primary: 60C05: Combinatorial probability 05C80: Random graphs 90B15: Network models, stochastic
Type
Part 4. Random graphs and particle systems
Information
Journal of Applied Probability , Volume 51 , Issue A: Celebrating 50 Years of The Applied Probability Trust , December 2014 , pp. 101 - 121
Copyright
Copyright © Applied Probability Trust 2014 

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