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The extinction time of a subcritical branching process related to the SIR epidemic on a random graph

  • Peter Windridge (a1)

Abstract

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.

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Current address: HSBC, 8 Canada Square, London, E14 5HQ, UK. Email address: pete@windridge.org.uk

References

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[2] Bohman, T. and Picollelli, M. (2012). SIR epidemics on random graphs with a fixed degree sequence. Random Structures Algorithms 41, 179214.
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