Journal of Applied Probability

The front of the epidemic spread and first passage percolation

Shankar Bhamidi, Remco van der Hofstad, and Júlia Komjáthy


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.

Article information

J. Appl. Probab., Volume 51A (2014), 101-121.

First available in Project Euclid: 2 December 2014

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Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability 05C80: Random graphs [See also 60B20] 90B15: Network models, stochastic

Flow random graph random network epidemics on random graphs first passage percolation hop count interacting particle system


Bhamidi, Shankar; van der Hofstad, Remco; Komjáthy, Júlia. The front of the epidemic spread and first passage percolation. J. Appl. Probab. 51A (2014), 101--121. doi:10.1239/jap/1417528470.

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