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Epidemics and vaccination on weighted graphs
Stockholm University, Faculty of Science, Department of Mathematics.
2011 (English)In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 232, no 1, 57-65 p.Article in journal (Refereed) Published
Abstract [en]

A Reed-Frost epidemic with inhomogeneous infection probabilities on a graph with prescribed degree distribution is studied. Each edge (u, v) in the graph is equipped with two weights W((u,v)) and W((v,u)) that represent the (subjective) strength of the connection and determine the probability that u infects v in case u is infected and vice versa. Expressions for the epidemic threshold are derived for i.i.d. weights and for weights that are functions of the degrees. For i.i.d. weights, a variation of the so called acquaintance vaccination strategy is analyzed where vertices are chosen randomly and neighbors of these vertices with large edge weights are vaccinated. This strategy is shown to outperform the strategy where the neighbors are chosen randomly in the sense that the basic reproduction number is smaller for a given vaccination coverage.

Place, publisher, year, edition, pages
2011. Vol. 232, no 1, 57-65 p.
Keyword [en]
Reed-Frost epidemic, Weighted graph, Degree distribution, Epidemic threshold, Vaccination
National Category
URN: urn:nbn:se:su:diva-66964DOI: 10.1016/j.mbs.2011.04.003ISI: 000292580900007OAI: diva2:470243
authorCount :1Available from: 2011-12-28 Created: 2011-12-22 Last updated: 2011-12-28Bibliographically approved

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Deijfen, Maria
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