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Graphs with specified degree distributions, simple epidemics and local vaccination strategies
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2007 (English)In: Advances in Applied Probability, ISSN 0001-8678, E-ISSN 1475-6064, Vol. 39, no 4, 922-948 p.Article in journal (Refereed) Published
Abstract [en]

Consider a random graph, having a prespecified degree distribution F, but other than that being uniformly distributed, describing the social structure (friendship) in a large community. Suppose that one individual in the community is externally infected by an infectious disease and that the disease has its course by assuming that infected individuals infect their not yet infected friends independently with probability p. For this situation, we determine the values of R-0, the basic reproduction number, and tau(0), the asymptotic final size in the case of a major outbreak. Furthermore, we examine some different local vaccination strategies, where individuals are chosen randomly and vaccinated, or friends of the selected individuals are vaccinated, prior to the introduction of the disease. For the studied vaccination strategies, we determine R-v, the reproduction number, and tau(v), the asymptotic final proportion infected in the case of a major outbreak, after vaccinating a fraction v.

Place, publisher, year, edition, pages
2007. Vol. 39, no 4, 922-948 p.
Keyword [en]
degree distribution, epidemic model, final size, limit theorem, networks, random graph, vaccination
National Category
URN: urn:nbn:se:uu:diva-12751DOI: 10.1239/aap/1198177233ISI: 000253218900006OAI: oai:DiVA.org:uu-12751DiVA: diva2:40520
Available from: 2008-01-11 Created: 2008-01-11 Last updated: 2010-05-12Bibliographically approved

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Publisher's full texthttp://arxiv1.library.cornell.edu/abs/math/0702021v1

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Janson, Svante
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