CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt167",{id:"formSmash:upper:j_idt167",widgetVar:"widget_formSmash_upper_j_idt167",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt172_j_idt174",{id:"formSmash:upper:j_idt172:j_idt174",widgetVar:"widget_formSmash_upper_j_idt172_j_idt174",target:"formSmash:upper:j_idt172:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

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});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
2017 (English)In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 74, no 4, p. 843-886Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

SPRINGER HEIDELBERG , 2017. Vol. 74, no 4, p. 843-886
##### Keywords [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, id: diva2:1089506
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt609",{id:"formSmash:j_idt609",widgetVar:"widget_formSmash_j_idt609",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt616",{id:"formSmash:j_idt616",widgetVar:"widget_formSmash_j_idt616",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt622",{id:"formSmash:j_idt622",widgetVar:"widget_formSmash_j_idt622",multiple:true});
##### Funder

Knut and Alice Wallenberg FoundationAvailable 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.

doi
pubmed
urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1938",{id:"formSmash:j_idt1938",widgetVar:"widget_formSmash_j_idt1938",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt2044",{id:"formSmash:lower:j_idt2044",widgetVar:"widget_formSmash_lower_j_idt2044",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt2045_j_idt2047",{id:"formSmash:lower:j_idt2045:j_idt2047",widgetVar:"widget_formSmash_lower_j_idt2045_j_idt2047",target:"formSmash:lower:j_idt2045:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});