Journal of Applied Probability: Volume 52 - Issue 4

The extinction time of a subcritical branching process related to the SIR epidemic on a random graph
Part of:
- Markov processes
- Graph theory
Peter Windridge
Published online by Cambridge University Press:

30 March 2016, pp. 1195-1201
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We give an exponential tail approximation for the extinction time of a subcritical multitype branching process arising from the SIR epidemic model on a random graph with given degrees, where the type corresponds to the vertex degree. As a corollary we obtain a Gumbel limit law for the extinction time, when beginning with a large population. Our contribution is to allow countably many types (this corresponds to unbounded degrees in the random graph epidemic model, as the number of vertices tends to∞). We only require a second moment for the offspring-type distribution featuring in our model.

Journal of Applied Probability