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Near-critical SIR epidemic on a random graph with given degreesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 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]

##### 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
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt431",{id:"formSmash:j_idt431",widgetVar:"widget_formSmash_j_idt431",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt437",{id:"formSmash:j_idt437",widgetVar:"widget_formSmash_j_idt437",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt443",{id:"formSmash:j_idt443",widgetVar:"widget_formSmash_j_idt443",multiple:true});
##### Funder

Knut and Alice Wallenberg Foundation
Available from: 2017-04-20 Created: 2017-04-20 Last updated: 2017-04-20Bibliographically approved

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.

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