# American Institute of Mathematical Sciences

2007, 4(2): 159-175. doi: 10.3934/mbe.2007.4.159

## A final size relation for epidemic models

 1 Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada 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  May 2006 Revised  October 2006 Published  February 2007

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. Mathematical Biosciences & Engineering, 2007, 4 (2) : 159-175. doi: 10.3934/mbe.2007.4.159
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