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Epidemics on a weighted network with tunable degree-degree correlation
Stockholm University, Faculty of Science, Department of Mathematics.
2014 (English)In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 253, 40-49 p.Article in journal (Refereed) Published
Abstract [en]

We propose a weighted version of the standard configuration model which allows for a tunable degree-degree correlation. A social network is modeled by a weighted graph generated by this model, where the edge weights indicate the intensity or type of contact between the individuals. An inhomogeneous Reed-Frost epidemic model is then defined on the network, where the inhomogeneity refers to different disease transmission probabilities related to the edge weights. By tuning the model we study the impact of different correlation patterns on the network and epidemics therein. Our results suggest that the basic reproduction number R-0 of the epidemic increases (decreases) when the degree-degree correlation coefficient rho increases (decreases). Furthermore, we show that such effect can be amplified or mitigated depending on the relation between degree and weight distributions as well as the choice of the disease transmission probabilities. In addition, for a more general model allowing additional heterogeneity in the disease transmission probabilities we show that rho can have the opposite effect on R-0.

Place, publisher, year, edition, pages
2014. Vol. 253, 40-49 p.
Keyword [en]
Branching processes, Configuration model, Weighted graph, Epidemic threshold, Degree-degree correlation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-106327DOI: 10.1016/j.mbs.2014.03.013ISI: 000337874100006OAI: oai:DiVA.org:su-106327DiVA: diva2:736555
Note

AuthorCount:1;

Available from: 2014-08-07 Created: 2014-08-04 Last updated: 2017-12-05Bibliographically approved
In thesis
1. Spatial Marriage Problems and Epidemics
Open this publication in new window or tab >>Spatial Marriage Problems and Epidemics
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of four papers covering three different topics on the modeling of large real networks and phenomena thereon. In Papers I and II, we propose and study the properties of a bipartite version of the model introduced by Deijfen, Holroyd and Häggström for generating translation-invariant spatial random graphs with prescribed degree distribution. In particular, we focus our attention on spatial random graphs generated by a matching scheme based on the Gale-Shapley stable marriage problem. In paper III, we propose a random graph model for generating edge-weighted graphs with prescribed degree and weight distributions, and tunable degree-degree correlation. We then study a simple inhomogeneous epidemic model on such graphs, where the infection probabilities are functions of the edge-weights, and investigate how the epidemic threshold is affected by the degree-degree correlation. In paper IV, we study a simple stochastic model aimed at representing a competition between two virus strains in a population. A longstanding principle in ecology known as the competitive exclusion principle predicts that when one of the strains has even the slightest advantage over the other, the one with the advantage will either drive the competitor to extinction or lead to a transformation in the ecological niche. We investigate how long it will take for the strain to drive its competitor to extinction.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University, 2014. 25 p.
National Category
Mathematics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-106796 (URN)978-91-7447-970-6 (ISBN)
Public defence
2014-09-24, sal 14, hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 1: In press. Paper 4: Manuscript.

Available from: 2014-09-02 Created: 2014-08-20 Last updated: 2015-03-27Bibliographically approved

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