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
收藏
页码：169 / 186
页数：18
相关论文
共 20 条
  • [1] Seasonality and the dynamics of infectious diseases
    Altizer, S
    Dobson, A
    Hosseini, P
    Hudson, P
    Pascual, M
    Rohani, P
    [J]. 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
    Cooke, K
    van den Driessche, P
    Zou, X
    [J]. 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
    Earn, DJD
    Rohani, P
    Bolker, BM
    Grenfell, BT
    [J]. SCIENCE, 2000, 287 (5453) : 667 - 670
  • [8] Seasonal infectious disease epidemiology
    Grassly, Nicholas C.
    Fraser, Christophe
    [J]. 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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