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}
}
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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