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An epidemic model with infector and exposure dependent severity
Stockholm University, Faculty of Science, Department of Mathematics.
2009 (English)In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 218, no 2, 105-120 p.Article in journal (Refereed) Published
Abstract [en]

A stochastic epidemic model allowing for both mildly and severely infectious individuals is defined, where an individual can become severely infectious directly upon infection or if additionally exposed to infection. It is shown that, assuming a large community, the initial phase of the epidemic may be approximated by a suitable branching process and that the main part of an epidemic that becomes established admits a law of large numbers and a central limit theorem, leading to a normal approximation for the final outcome of such an epidemic. Effects of vaccination prior to an outbreak are studied and the critical vaccination coverage, above which only small outbreaks can occur, is derived. The results are illustrated by simulations that demonstrate that the branching process and normal approximations work well for finite communities, and by numerical examples showing that the final outcome may be close to discontinuous in certain model parameters and that the fraction mildly infected may actually increase as an effect of vaccination.

Place, publisher, year, edition, pages
2009. Vol. 218, no 2, 105-120 p.
Keyword [en]
Stochastic epidemic, Final size, Basic reproduction number, Severity, Exposure, Vaccination
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
URN: urn:nbn:se:su:diva-34928DOI: 10.1016/j.mbs.2009.01.003ISI: 000265362200005OAI: diva2:285970
Available from: 2010-01-13 Created: 2010-01-13 Last updated: 2011-04-04Bibliographically approved

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