The extinction time of a subcritical branching process related to the SIR epidemic on a random graph. (December 2015)

• Record Type: Journal Article
• Authors: Windridge, Peter
• Is Part Of: Journal of applied probability. Volume 52:Number 4(2015)
• Page Start: 1195
• Page End: 1201
• Publication Date: 2015-12
• Subjects: Multitype branching process, -- exponential tail approximation, -- Gumbel, -- SIR epidemic; 60J80, -- 92D30, -- 05C80, -- 60J28; 519.2
• DOI: 10.1239/jap/1450802763
• Languages: English
• ISSNs: 0021-9002

Abstract

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.