TY - JOUR
T1 - The front of the epidemic spread and first passage percolation
AU - Bhamidi, S.
AU - Hofstad, van der, R.W.
AU - Komjáthy, J.
PY - 2014
Y1 - 2014
N2 - 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 ¿ 8, with an appropriate X2log+X condition. We also study the epidemic trail between the source and typical vertices in the graph.
AB - 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 ¿ 8, with an appropriate X2log+X condition. We also study the epidemic trail between the source and typical vertices in the graph.
U2 - 10.1239/jap/1417528470
DO - 10.1239/jap/1417528470
M3 - Article
SN - 0021-9002
VL - 51A
SP - 101
EP - 121
JO - Journal of Applied Probability
JF - Journal of Applied Probability
ER -