Global threshold dynamics of an SVIR model with age-dependent infection and relapse

被引：6

作者：

Wang, Jinliang ^{[1
]}

Lang, Jiying ^{[1
]}

Chen, Yuming ^{[2
]}

机构：

[1] Heilongjiang Univ, Sch Math Sci, Harbin, Peoples R China

[2] Wilfrid Laurier Univ, Dept Math, Waterloo, ON, Canada

来源：

JOURNAL OF BIOLOGICAL DYNAMICS | 2017年 / 11卷

基金：

加拿大自然科学与工程研究理事会; 中国国家自然科学基金;

关键词：

SVIR model; basic reproduction number; global stability; infection age; relapse age; SEIR EPIDEMIOLOGIC MODEL; VARYING INFECTIVITY; INFINITE DELAY; HIV-INFECTION; STABILITY; VACCINATION; DISEASES; LATENCY;

D O I：

10.1080/17513758.2016.1226436

中图分类号：

Q14 [生态学（生物生态学）];

学科分类号：

071012 ; 0713 ;

摘要：

A susceptible-vaccinated-infectious-recovered epidemic model with infection age and relapse age has been formulated. We first address the asymptotic smoothness of the solution semiflow, existence of a global attractor, and uniform persistence of the model. Then by constructing suitable Volterra-type Lyapunov functionals, we establish a global threshold dynamics of the model, which is determined by the basic reproduction number. Biologically, it is confirmed that neglecting the possibility of vaccinees getting infected will over-estimate the effect of vaccination strategies. The obtained results generalize some existing ones.

引用

页码：427 / 454

页数：28

共 33 条

[11] SVIR epidemic models with vaccination strategies [J].

Liu, Xianning ;

Takeuchi, Yasuhiro ;

Iwami, Shingo .

JOURNAL OF THEORETICAL BIOLOGY, 2008, 253 (01) :1-11

[12] Lyapunov functional and global asymptotic stability for an infection-age model [J].

Magal, P. ;

McCluskey, C. C. ;

Webb, G. F. .

APPLICABLE ANALYSIS, 2010, 89 (07) :1109-1140

[13] Variational bounds and sensitivity analysis of traffic processes in continuous flow models [J].

Wardi, Y ;

Melamed, B .

DISCRETE EVENT DYNAMIC SYSTEMS-THEORY AND APPLICATIONS, 2001, 11 (03) :249-282

[14] TWO-GROUP INFECTION AGE MODEL INCLUDING AN APPLICATION TO NOSOCOMIAL INFECTION [J].

Magal, Pierre ;

McCluskey, Connell .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2013, 73 (02) :1058-1095

[15] GLOBAL STABILITY FOR AN SEI EPIDEMIOLOGIGAL MODEL WITH CONTINUOUS AGE-STRUCTURE IN THE EXPOSED AND INFECTIOUS CLASSES [J].

McCluskey, C. Connell .

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 2012, 9 (04) :819-841

[16] GLOBAL STABILITY FOR AN SEIR EPIDEMIOLOGICAL MODEL WITH VARYING INFECTIVITY AND INFINITE DELAY [J].

McCluskey, C. Connell .

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 2009, 6 (03) :603-610

[17] An age-structured model of HIV infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells [J].

Nelson, PW ;

Gilchrist, MA ;

Coombs, D ;

Hyman, JM ;

Perelson, AS .

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 2004, 1 (02) :267-288

[18]

Röst G, 2008, MATH BIOSCI ENG, V5, P389

[19] Mathematical analysis of age-structured HIV-1 dynamics with combination antiretroviral therapy [J].

Rong, Libin ;

Feng, Zhilan ;

Perelson, Alan S. .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2007, 67 (03) :731-756

[20]

Smith H L., 2011, Dynamical Systems and Population Persistence

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