张道祥,熊书琴

• 1:安徽师范大学数学与计算机科学学院

摘要(Abstract)：

本文提出了一个双时滞SIRS模型.通过分析相应的特征方程并利用Hurwitz矩阵相关定理,讨论了无病平衡点和地方平衡点的局部稳定性.当基本再生数满足R0>1时,证明了系统的持久性.所得结果改进和扩展了文献中的相应结果.

关键词(KeyWords)： SIRS疾病模型;局部稳定性;持久性;双时滞

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金资助项目(11302002);; 数学天元青年基金资助项目(11126237);; 安徽省高校优秀青年人才基金资助项目(2011SQRL022ZD)

作者(Author): 张道祥,熊书琴

参考文献(References)：

• [1]K L Cooke.Stability analysis for a vector disease model[J].Rocky Mountain J.Math,1979,9:31-42.
• [2]XU Rui,MA Zhi-en.Global stability of a SIR epidemic model with nonlinear incidence rate and time delay[J].Nonlinear Anal,2009,10:3 175-3 189.
• [3]ZHANG Tai-lei,TENG Zhi-dong.Global behavior and permanence of SIRS epidemic model with time delay[J].Nonlinear Anal,2008,9:1 409-1 424.
• [4]李玉洁,张道祥.具有变时滞的五种Lotka-Volterra混合系统的正周期解[J].数学杂志,2011,31(3):433-439.
• [5]连晓飞,周文,曹磊.具有脉冲出生和垂直传染的双时滞SERIS传染病模型[J].安徽工程大学学报:自然科学版,2014,29(2):90-94.
• [6]尹红云,董冉冉,张道祥.一类具有饱和发病率与暂时免疫的时滞SIRS模型[J].安徽师范大学学报:自然科学版,2012,35(2):115-118.
• [7]卢雪娟,王伟华,堵秀芬.一类具有双时滞的SEIRSD传染病模型的分析[J].数学的实践与认识,2010,40(22):135-142.
• [8]K Hattaf,A A Lashari,Y Louartassi,et al.A delays SIR epidemic model with general incidence rate[J].Electronic Journal,2013,3:1-9.
• [9]ZHANG Tong-qian,MENG Xin-zhu,ZHANG Tong-hua,et al.Global dynamics for a new highdimensional SIR model with distributed delay[J].Applied Mathematics and Computation,2012,218:11 806-11 819.
• [10]JIN Zhen,MA Zhi-en,HAN Mao-an.Global stability of an SIRS epidemic model with delays[J].Acta Mathematica Scientia,1993,26B(2):291-306.
• [11]SONG Mei,MA Wan-biao,Y Takeuchi.Permanence of a delayed SIR epidemic model density dependent birth rate[J].J.Math,2007,201:389-394.
• [12]MA Wan-biao,Y Takeuchi,T Hara,et al.Permanence of an SIR epidemic model with time delays[J].Tohoku Math.J,2002,54:581-591.
• [13]马知恩,周义仓.常微分方程定性与稳定性方法[M].北京:科学出版社,2001.