A final size relation for epidemic models

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

doi:10.3934/mbe.2007.4.159

Mathematical Biosciences and Engineering

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: 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.

Keywords:

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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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.

A correction on

Deaths in Immigration and Customs Enforcement (ICE) detention: FY2018–2020

By Sophie Terp, Sameer Ahmed, Elizabeth Burner, Madeline Ross, Molly Grassini, Briah Fischer, Parveen Parmar. Deaths in Immigration and Customs Enforcement (ICE) detention: FY2018–2020[J]. AIMS Public Health, 2021, 8(1): 81–89. doi: 10.3934/publichealth.2021006.

We would like to submit the following correction to our recently published paper due to the wrong of reference 8. The details as the following.

8. Congress.gov (2018) H. Rept. 115–239—Department OF Homeland Security Appropriations Bill, 2018. Available from: https://www.congress.gov/congressional-report/115th-congress/house-report/239.
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