Contact process on a graph with communities

2012/10/12 by Sivakoff, David · 1 citation
#60G55 (Primary) 05C82 #91D30 (Secondary) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1210.3434

Abstract

We are interested in the spread of an epidemic between two communities that have higher connectivity within than between them. We model the two communities as independent Erdos-Renyi random graphs, each with n vertices and edge probability p = n^a-1 (0 1 then the contact process on the Erdos-Renyi random graph is supercritical, and we show that it survives for exponentially long. Further, let τbe the time to infect a positive fraction of vertices in the second community when the infection starts from a single vertex in the first community. We show that on the event that the contact process survives exponentially long, τ|B|/(np) converges in distribution to an exponential random variable with a specified rate. These results generalize to a graph with N communities.

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