# Law of large numbers for the SIR epidemic on a random graph with given degrees

@article{Janson2014LawOL,
title={Law of large numbers for the SIR epidemic on a random graph with given degrees},
author={Svante Janson and Malwina J. Luczak and Peter Windridge},
journal={Random Structures \& Algorithms},
year={2014},
volume={45}
}
• Published 26 August 2013
• Mathematics
• Random Structures & Algorithms
We study the susceptible‐infective‐recovered (SIR) epidemic on a random graph chosen uniformly subject to having given vertex degrees. In this model infective vertices infect each of their susceptible neighbours, and recover, at a constant rate. Suppose that initially there are only a few infective vertices. We prove there is a threshold for a parameter involving the rates and vertex degrees below which only a small number of infections occur. Above the threshold a large outbreak occurs with…

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