Lyapunov functional and global asymptotic stability for an infection-age model

被引：263

作者：

Magal, P. ^{[2
]}

McCluskey, C. C. ^{[1
]}

Webb, G. F. ^{[3
]}

机构：

[1] Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada

[2] Univ Le Havre, Dept Math, F-76058 Le Havre, France

[3] Vanderbilt Univ, Dept Math, Stevenson Ctr 1326, Nashville, TN 37240 USA

来源：

APPLICABLE ANALYSIS | 2010年 / 89卷 / 07期

关键词：

Lyapunov functional; structured population; global stability; age of infection; integrated semigroup; SEIR EPIDEMIOLOGIC MODEL; VARYING INFECTIVITY; NONLINEAR INCIDENCE; VIRUS DYNAMICS; SIR; SYSTEMS;

D O I：

10.1080/00036810903208122

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study an infection-age model of disease transmission, where both the infectiousness and the removal rate may depend on the infection age. In order to study persistence, the system is described using integrated semigroups. If the basic reproduction number R0 1, then the disease-free equilibrium is globally asymptotically stable. For R0 1, a Lyapunov functional is used to show that the unique endemic equilibrium is globally stable amongst solutions for which disease transmission occurs.

引用

页码：1109 / 1140

页数：32

共 60 条

[11] Essential growth rate for bounded linear perturbation of non-densely defined Cauchy problems [J].

Ducrot, A. ;

Liu, Z. ;

Magal, P. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 341 (01) :501-518

[12]

Engel K.-J., 1999, One-parameter semigroups for linear evolution equations, V194

[13] Global stability for a virus dynamics model with nonlinear incidence of infection and removal [J].

Georgescu, Paul ;

Hsieh, Ying-Hen .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2006, 67 (02) :337-353

[14] A graph-theoretic approach to the method of global Lyapunov functions [J].

Guo, Hongbin ;

Li, Michael Y. ;

Shuai, Zhisheng .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (08) :2793-2802

[15] Global dynamics of a staged progression model for infectious diseases [J].

Guo, Hongbin ;

Li, Michael Y. .

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 2006, 3 (03) :513-525

[16]

Hale J. K., 1988, Asymptotic Behavior of Dissipative Systems

[17] PERSISTENCE IN INFINITE-DIMENSIONAL SYSTEMS [J].

HALE, JK ;

WALTMAN, P .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1989, 20 (02) :388-395

[18]

HETHCOTE H W, 1976, Mathematical Biosciences, V28, P335, DOI 10.1016/0025-5564(76)90132-2

[19]

Hethcote HerbertW., 1989, AppliedMathematical Ecology, V18, P119, DOI [DOI 10.1007/978-3-642-61317-3_5, 10.1007/978-3-642-61317-35, DOI 10.1007/978-3-642-61317-35, 10.1007/978-3-642-61317-3_5]

[20] The mathematics of infectious diseases [J].

Hethcote, HW .

SIAM REVIEW, 2000, 42 (04) :599-653

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