Journal of Applied Probability

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

Peter Windridge

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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.

Article information

Source
J. Appl. Probab., Volume 52, Number 4 (2015), 1195-1201.

Dates
First available in Project Euclid: 22 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.jap/1450802763

Digital Object Identifier
doi:10.1239/jap/1450802763

Mathematical Reviews number (MathSciNet)
MR3439182

Zentralblatt MATH identifier
1342.60150

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 92D30: Epidemiology
Secondary: 05C80: Random graphs [See also 60B20] 60J28: Applications of continuous-time Markov processes on discrete state spaces

Keywords
Multitype branching process exponential tail approximation Gumbel SIR epidemic

Citation

Windridge, Peter. The extinction time of a subcritical branching process related to the SIR epidemic on a random graph. J. Appl. Probab. 52 (2015), no. 4, 1195--1201. doi:10.1239/jap/1450802763. https://projecteuclid.org/euclid.jap/1450802763


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References

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