Global stability of a delayed epidemic model with latent period and vaccination strategy

被引：38

作者：

Xu, Rui ^{[1
]}

机构：

[1] Shijiazhuang Mech Engn Coll, Inst Appl Math, Shijiazhuang 050003, Hebei Province, Peoples R China

来源：

APPLIED MATHEMATICAL MODELLING | 2012年 / 36卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Latent period; Vaccination; Time delay; Global stability; PULSE VACCINATION; BACKWARD BIFURCATION; NONLINEAR INCIDENCE; SEIR MODEL; IMMUNITY; TRANSMISSION; DYNAMICS; DISEASES;

D O I：

10.1016/j.apm.2011.12.037

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, a mathematical model describing the transmission dynamics of an infectious disease with an exposed (latent) period and waning vaccine-induced immunity is investigated. The basic reproduction number is found by applying the method of the next generation matrix. It is shown that the global dynamics of the model is completely determined by the basic reproduction number. By means of appropriate Lyapunov functionals and LaSalle's invariance principle, it is proven that if the basic reproduction number is less than or equal to unity, the disease-free equilibrium is globally asymptotically stable and the disease fades out; and if the basic reproduction number is greater than unity, the endemic equilibrium is globally asymptotically stable and therefore the disease becomes endemic. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：5293 / 5300

页数：8

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