# Contact process on a graph with communities

@article{Sivakoff2012ContactPO, title={Contact process on a graph with communities}, author={David Sivakoff}, journal={arXiv: Probability}, year={2012} }

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 \tau be the time to infect a positive fraction of vertices in the second community when the infectionâ€¦Â Expand

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