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December 2015 The extinction time of a subcritical branching process related to the SIR epidemic on a random graph
Peter Windridge
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J. Appl. Probab. 52(4): 1195-1201 (December 2015). DOI: 10.1239/jap/1450802763

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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Peter Windridge. "The extinction time of a subcritical branching process related to the SIR epidemic on a random graph." J. Appl. Probab. 52 (4) 1195 - 1201, December 2015. https://doi.org/10.1239/jap/1450802763

Information

Published: December 2015
First available in Project Euclid: 22 December 2015

zbMATH: 1342.60150
MathSciNet: MR3439182
Digital Object Identifier: 10.1239/jap/1450802763

Subjects:
Primary: 60J80, 92D30
Secondary: 05C80, 60J28

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 4 • December 2015
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