A final size relation for epidemic models

被引：106

作者：

Arino, Julien ^{[1
]}

Brauer, Fred

van den Driessche, P.

Watmough, James

Wu, Jianhong

机构：

[1] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada

[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

[3] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3P4, Canada

[4] Univ New Brunswick, Dept Math & Stat, Fredericton, NB E3B 5A3, Canada

[5] York Univ, Dept Math & Stat, N York, ON M3J 1P3, Canada

来源：

MATHEMATICAL BIOSCIENCES AND ENGINEERING | 2007年 / 4卷 / 02期

关键词：

epidemic models; basic reproduction number; final size relation; vertical transmission;

D O I：

10.3934/mbe.2007.4.159

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

A final size relation is derived for a general class of epidemic mode ls, 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 reprod uction number in models with vertical transmission. Applications are given to specific models for influenza and SARS.

引用

页码：159 / 175

页数：17

共 16 条

[1]

ANDERSON R M, 1991

[2]

[Anonymous], 1994, CLASSICS APPL MATH

[3] Simple models for containment of a pandemic [J].

Arino, Julien ;

Brauer, Fred ;

van den Driessche, P. ;

Watmough, James ;

Wu, Jianhong .

JOURNAL OF THE ROYAL SOCIETY INTERFACE, 2006, 3 (08) :453-457

[4]

Brauer F, 2006, MATH BIOSCI ENG, V3, P1

[5] Models for transmission of disease with immigration of infectives [J].

Brauer, F ;

van den Driessche, P .

MATHEMATICAL BIOSCIENCES, 2001, 171 (02) :143-154

[6]

Busenberg S, 1993, Vertically transmitted diseases: models and dynamics, V23

[7]

DIEKMANN O, 1990, J MATH BIOL, V28, P365

[8]

Diekmann O., 2000, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis, and Interpretation

[9] Modelling strategies for controlling SARS outbreaks [J].

Gumel, AB ;

Ruan, SG ;

Day, T ;

Watmough, J ;

Brauer, F ;

van den Driessche, P ;

Gabrielson, D ;

Bowman, C ;

Alexander, ME ;

Ardal, S ;

Wu, JH ;

Sahai, BM .

PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES, 2004, 271 (1554) :2223-2232

[10] Contribution to the mathematical theory of epidemics [J].

Kermack, WO ;

McKendrick, AG .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-CONTAINING PAPERS OF A MATHEMATICAL AND PHYSICAL CHARACTER, 1927, 115 (772) :700-721

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