A final size relation for epidemic models

Julien Arino; Fred Brauer; P. van den Driessche; James Watmough; Jianhong Wu

doi:10.3934/mbe.2007.4.159

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2007, Volume 4, Issue 2: 159-175. Doi: 10.3934/mbe.2007.4.159

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A final size relation for epidemic models

1.
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2
2.
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2
3.
Department of Mathematics and Statistics, University of Victoria, Victoria B.C., Canada V8W 3P4
4.
Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3
5.
Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3

Received: April 30, 2006

Revised: September 30, 2006

Published: January 2007

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Abstract

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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Mathematics Subject Classification: 92D30.

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