University Library
  • Login
A gateway to Melbourne's research publications
Minerva Access is the University's Institutional Repository. It aims to collect, preserve, and showcase the intellectual output of staff and students of the University of Melbourne for a global audience.
View Item 
  • Minerva Access
  • Science
  • School of Mathematics and Statistics
  • School of Mathematics and Statistics - Research Publications
  • View Item
  • Minerva Access
  • Science
  • School of Mathematics and Statistics
  • School of Mathematics and Statistics - Research Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

    Near-critical SIR epidemic on a random graph with given degrees

    Thumbnail
    Download
    Published version (1.467Mb)

    Citations
    Scopus
    Web of Science
    Altmetric
    1
    1
    Author
    Janson, S; Luczak, M; Windridge, P; House, T
    Date
    2017-03-01
    Source Title
    Journal of Mathematical Biology
    Publisher
    SPRINGER HEIDELBERG
    University of Melbourne Author/s
    Luczak, Malwina
    Affiliation
    School of Mathematics and Statistics
    Metadata
    Show full item record
    Document Type
    Journal Article
    Citations
    Janson, S., Luczak, M., Windridge, P. & House, T. (2017). Near-critical SIR epidemic on a random graph with given degrees. JOURNAL OF MATHEMATICAL BIOLOGY, 74 (4), pp.843-886. https://doi.org/10.1007/s00285-016-1043-z.
    Access Status
    Open Access
    URI
    http://hdl.handle.net/11343/254813
    DOI
    10.1007/s00285-016-1043-z
    Abstract
    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 [Formula: see text], with [Formula: see text] 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 [Formula: see text]. 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.

    Export Reference in RIS Format     

    Endnote

    • Click on "Export Reference in RIS Format" and choose "open with... Endnote".

    Refworks

    • Click on "Export Reference in RIS Format". Login to Refworks, go to References => Import References


    Collections
    • Minerva Elements Records [52443]
    • School of Mathematics and Statistics - Research Publications [840]
    Minerva AccessDepositing Your Work (for University of Melbourne Staff and Students)NewsFAQs

    BrowseCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects
    My AccountLoginRegister
    StatisticsMost Popular ItemsStatistics by CountryMost Popular Authors