A final size relation for epidemic models

  • Received: 01 May 2006 Accepted: 29 June 2018 Published: 01 February 2007
  • MSC : 92D30.

  • A final size relation is derived for a general class of epidemic models, including models with multiple susceptible classes. The derivation depends on an explicit formula for the basic reproduction number of a general class of disease transmission models, which is extended to calculate the basic reproduction number in models with vertical transmission. Applications are given to specific models for influenza and SARS.

    Citation: Julien Arino, Fred Brauer, P. van den Driessche, James Watmough, Jianhong Wu. A final size relation for epidemic models[J]. Mathematical Biosciences and Engineering, 2007, 4(2): 159-175. doi: 10.3934/mbe.2007.4.159

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  • A final size relation is derived for a general class of epidemic models, including models with multiple susceptible classes. The derivation depends on an explicit formula for the basic reproduction number of a general class of disease transmission models, which is extended to calculate the basic reproduction number in models with vertical transmission. Applications are given to specific models for influenza and SARS.


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  • © 2007 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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