THRESHOLD DYNAMICS IN A TIME-DELAYED PERIODIC SIS EPIDEMIC MODEL

被引：38

作者：

Lou, Yijun ^{[1
]}

Zhao, Xiao-Qiang ^{[1
]}

机构：

[1] Mem Univ Newfoundland, Dept Math, St John, NF A1C 5S7, Canada

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2009年 / 12卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Periodic epidemic model; Maturation delay; Basic reproduction ratio; Periodic solutions; Uniform persistence; MONOTONE;

D O I：

10.3934/dcdsb.2009.12.169

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The global dynamics of a periodic SIS epidemic model with maturation delay is investigated. We first obtain sufficient conditions for the single population growth equation to admit a globally attractive positive periodic solution. Then we introduce the basic reproduction ratio R-0 for the epidemic model, and show that the disease dies out when R-0 < 1, and the disease remains endemic when R-0 > 1. Numerical simulations are also provided to confirm our analytic results.

引用

页码：169 / 186

页数：18

共 20 条

[1] Seasonality and the dynamics of infectious diseases [J].

Altizer, S ;

Dobson, A ;

Hosseini, P ;

Hudson, P ;

Pascual, M ;

Rohani, P .

ECOLOGY LETTERS, 2006, 9 (04) :467-484

[2]

ANDERSON R M, 1991

[3]

[Anonymous], 2000, Mathematical epidemiology of infectious diseases: model building, analysis, and interpretation

[4]

[Anonymous], AM MATH SOC MATH SUR

[5] Interaction of maturation delay and nonlinear birth in population and epidemic models [J].

Cooke, K ;

van den Driessche, P ;

Zou, X .

JOURNAL OF MATHEMATICAL BIOLOGY, 1999, 39 (04) :332-352

[6]

Dietz K., 1976, Proceedings of a Workshop on Mathematical Models in Medicine, P1

[7] A simple model for complex dynamical transitions in epidemics [J].

Earn, DJD ;

Rohani, P ;

Bolker, BM ;

Grenfell, BT .

SCIENCE, 2000, 287 (5453) :667-670

[8] Seasonal infectious disease epidemiology [J].

Grassly, Nicholas C. ;

Fraser, Christophe .

PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES, 2006, 273 (1600) :2541-2550

[9]

Hale J.K., 1988, MATH SURVEYS MONOGR, V25

[10]

Hale J.K., 1993, Introduction to Functional Differential Equations

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