Change search
ReferencesLink to record
Permanent link

Direct link
A weighted configuration model and inhomogeneous epidemics
Stockholm University, Faculty of Science, Department of Mathematics. (Matematiska institutionen)
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Social Sciences, Department of Sociology.
2011 (English)In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 145, 1368-1384 p.Article in journal (Refereed) Published
Abstract [en]

A random graph model with prescribed degree distribution and degree dependent

edge weights is introduced. Each vertex is independently equipped with a random number

of half-edges and each half-edge is assigned an integer valued weight according to a distribution

that is allowed to depend on the degree of its vertex. Half-edges with the same weight

are then paired randomly to create edges. An expression for the threshold for the appearance

of a giant component in the resulting graph is derived using results on multi-type branching

processes. The same technique also gives an expression for the basic reproduction number

for an epidemic on the graph where the probability that a certain edge is used for transmission

is a function of the edge weight (reflecting how closely ‘connected’ the corresponding

vertices are). It is demonstrated that, if vertices with large degree tend to have large (small)

weights on their edges and if the transmission probability increases with the edge weight,

then it is easier (harder) for the epidemic to take off compared to a randomized epidemic

with the same degree and weight distribution. A recipe for calculating the probability of a

large outbreak in the epidemic and the size of such an outbreak is also given. Finally, the

model is fitted to three empirical weighted networks of importance for the spread of contagious

diseases and it is shown that


can be substantially over- or underestimated if the

correlation between degree and weight is not taken into account.

Place, publisher, year, edition, pages
2011. Vol. 145, 1368-1384 p.
National Category
Natural Sciences Physical Sciences Other Mathematics
Research subject
Mathematical Statistics
URN: urn:nbn:se:su:diva-69366DOI: 10.1007/s10955-011-0343-3ISI: 000297593900012OAI: diva2:476390
authorCount :3Available from: 2012-01-12 Created: 2012-01-12 Last updated: 2012-01-24Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Britton, TomDeijfen, MariaLiljeros, Fredrik
By organisation
Department of MathematicsDepartment of Sociology
In the same journal
Journal of statistical physics
Natural SciencesPhysical SciencesOther Mathematics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 66 hits
ReferencesLink to record
Permanent link

Direct link