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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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

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

First available in Project Euclid: 22 December 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Multitype branching process exponential tail approximation Gumbel SIR epidemic


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.

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