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

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

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 tim...

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Bibliographic Details
Published in:Journal of applied probability 2015-12, Vol.52 (4), p.1195-1201
Main Author: Windridge, Peter
Format: Article
Language:eng
Subjects:
05C80
60J28
60J80
92D30
Approximation
Branching (mathematics)
Epidemics
exponential tail approximation
Extinction
Graph representations
Graph theory
Graphs
Gumbel
Markov processes
Mathematical analysis
Mathematical models
Multitype branching process
Probability distribution
Short Communications
SIR epidemic
Studies
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Summary: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.
ISSN:0021-9002
1475-6072