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-R enyi random graphs, each with n vertices and edge probability p = n a 1 (0 1 then the contact process on the Erdos-R enyi random graph is supercritical, and we show that it survives for exponentially long. Further, let be the time to infect a positive fraction of vertices in the second community when the infection starts from a single vertex in the rst community. We show that on the event that the contact process survives exponentially long, jBj=(np) converges in distribution to an exponential random variable with a specied rate. These results generalize to a graph with N communities.
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