Qualitative analysis of an SIR epidemic model with stage structure

被引：26

作者：

Jia Jianwen ^{[1
]}

Li Qiuying ^{[2
]}

机构：

[1] Shanxi Normal Univ, Sch Math & Comp Sci, Linfen 041004, Peoples R China

[2] Yunchen Coll, Dept Appl Math, Shanxi 044000, Yuncheng, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2007年 / 193卷 / 01期

基金：

上海市自然科学基金;

关键词：

stage structure; SIR; epidemic; equilibrium; Liapunov functional persistence;

D O I：

10.1016/j.amc.2007.03.041

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An SIR epidemic model with stage structure consisting immature and mature stages is investigated. The global stability of epidemic equilibrium and disease-free equilibrium is proved. Meanwhile, we obtained that global dynamics is completely determined by the basic reproduction number sigma. If sigma < 1, the disease-free equilibrium is globally stable and the disease dies out. If sigma > 1, a unique endemic equilibrium is globally stable in the interior of a feasible region and the disease persists at endemic equilibrium. (C) 2007 Published by Elsevier Inc.

引用

页码：106 / 115

页数：10

共 13 条

[1] A TIME-DELAY MODEL OF SINGLE-SPECIES GROWTH WITH STAGE STRUCTURE [J].

AIELLO, WG ;

FREEDMAN, HI .

MATHEMATICAL BIOSCIENCES, 1990, 101 (02) :139-153

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

Brauer, F ;

van den Driessche, P .

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

[3] Analysis of an SEIRS epidemic model with two delays [J].

Cooke, KL ;

vandenDriessche, P .

JOURNAL OF MATHEMATICAL BIOLOGY, 1996, 35 (02) :240-260

[4]

COSTILLCHAVEZ C, 1995, MATH POPUL DYN, P33

[5]

Kuang Y., 1993, DELAY DIFFERENTIAL E

[6]

Li JQ, 2004, APPL MATH MECH-ENGL, V25, P396

[7] Optimal harvesting and stability for a two-species competitive system with stage structure [J].

Song, XY ;

Chen, LS .

MATHEMATICAL BIOSCIENCES, 2001, 170 (02) :173-186

[8]

Wang W, 2004, MATH BIOSCI, V190, P97, DOI [10.1016/j.mbs.2002.11.001, 10.1016/j.mbs.2004.11.001]

[9] Bifurcations in an epidemic model with constant removal rate of the infectives [J].

Wang, WD ;

Ruan, SG .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 291 (02) :775-793

[10]

Wang WD, 2002, NONLINEAR ANAL-REAL, V3, P365, DOI 10.1016/S1468-1218(01)00035-9

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