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Near-critical SIR epidemic on a random graph with given degrees
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Queen Mary Univ London, Sch Math Sci, Mile End Rd, London E1 4NS, England..
Queen Mary Univ London, Sch Math Sci, Mile End Rd, London E1 4NS, England..
Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England..
2017 (English)In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 74, no 4, 843-886 p.Article in journal (Refereed) Published
Abstract [en]

Emergence of new diseases and elimination of existing diseases is a key public health issue. In mathematical models of epidemics, such phenomena involve the process of infections and recoveries passing through a critical threshold where the basic reproductive ratio is 1. In this paper, we study near-critical behaviour in the context of a susceptible-infective-recovered epidemic on a random (multi)graph on n vertices with a given degree sequence. We concentrate on the regime just above the threshold for the emergence of a large epidemic, where the basic reproductive ratio is , with tending to infinity slowly as the population size, n, tends to infinity. We determine the probability that a large epidemic occurs, and the size of a large epidemic. Our results require basic regularity conditions on the degree sequences, and the assumption that the third moment of the degree of a random susceptible vertex stays uniformly bounded as . As a corollary, we determine the probability and size of a large near-critical epidemic on a standard binomial random graph in the 'sparse' regime, where the average degree is constant. As a further consequence of our method, we obtain an improved result on the size of the giant component in a random graph with given degrees just above the critical window, proving a conjecture by Janson and Luczak.

Place, publisher, year, edition, pages
SPRINGER HEIDELBERG , 2017. Vol. 74, no 4, 843-886 p.
Keyword [en]
SIR epidemic, Random graph with given degrees, Configuration model, Critical window
National Category
Biological Sciences Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-320409DOI: 10.1007/s00285-016-1043-zISI: 000394299200003PubMedID: 27475950OAI: oai:DiVA.org:uu-320409DiVA: diva2:1089506
Funder
Knut and Alice Wallenberg Foundation
Available from: 2017-04-20 Created: 2017-04-20 Last updated: 2017-04-20Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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