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Stochastic SIR epidemics in a population with households and schools
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 3
2016 (English)In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 72, no 5, p. 1177-1193Article in journal (Refereed) Published
Abstract [en]

We study the spread of stochastic SIR (Susceptible Infectious Recovered) epidemics in two types of structured populations, both consisting of schools and households. In each of the types, every individual is part of one school and one household. In the independent partition model, the partitions of the population into schools and households are independent of each other. This model corresponds to the well-studied household-workplace model. In the hierarchical model which we introduce here, members of the same household are also members of the same school. We introduce computable branching process approximations for both types of populations and use these to compare the probabilities of a large outbreak. The branching process approximation in the hierarchical model is novel and of independent interest. We prove by a coupling argument that if all households and schools have the same size, an epidemic spreads easier (in the sense that the number of individuals infected is stochastically larger) in the independent partition model. We also show by example that this result does not necessarily hold if households and/or schools do not all have the same size.

Place, publisher, year, edition, pages
2016. Vol. 72, no 5, p. 1177-1193
Keyword [en]
SIR epidemics, Structured populations, Branching processes, Coupling
National Category
Biological Sciences Mathematics
Identifiers
URN: urn:nbn:se:su:diva-128500DOI: 10.1007/s00285-015-0901-4ISI: 000371294400002PubMedID: 26070348OAI: oai:DiVA.org:su-128500DiVA: diva2:918413
Available from: 2016-04-11 Created: 2016-03-30 Last updated: 2017-11-30Bibliographically approved

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