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两种群相互竞争的高维SEIR传染病模型全局渐近稳定性 被引量：3

The global stability of a nonlinear high dimensional SEIR epidemic model of two competitive species
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摘要 研究了一类两种群相互竞争的非线性高维SEIR传染病数学模型动力学性质,综合利用Lasalle不变集原理,Lyapunov函数,Routh-Hurwitz判据和Krasnoselskii等多种方法,得到了边界平衡点的全局渐近稳定和正平衡点局部渐近稳定的阈值条件. Dynamic property about a nonlinear dimensional SEIR epidemic model of two competitive species isstudied. By using some methods, including Lasalle invariant set principle, Lyapunov function, Routh-Hurwitz criterion and Krasnoselskii technique etc., some threshold conditions are identified for the global stabilities of bounded equilibria and the local stability of positive equilibrium.
作者 徐文雄 张太雷 徐宗本
机构地区 西安交通大学理学院 新疆大学数学与系统科学学院
出处 《纯粹数学与应用数学》 CSCD 北大核心 2008年第2期209-219,共11页 Pure and Applied Mathematics
基金 国家自然科学基金重点项目(10531030) 国家"十五"医学科技攻关项目(2004BA719A01)
关键词 竞争系统 传染病 数学模型 闽值 渐近稳定性 competitive system, epidemic, mathematic model, threshold, asymptotic stability
分类号 O175.1 [理学—基础数学]
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参考文献14

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共引文献88

同被引文献23

  • 1赵文才,孟新柱.具有垂直传染的SIR脉冲预防接种模型[J].应用数学,2009,22(3):676-682. 被引量：7
  • 2韩丽涛.两种群相互竞争的具有脉冲出生率的SIS传染病模型[J].生物数学学报,2006,21(2):237-246. 被引量：5
  • 3Zhang Xiaobing, Huo Haifeng, Xiang Hong, et al.. An SIRS ep- idemic model with pulse vaccination and non - monotonic inci- dence rate[J]. Nonlinear Analysis: Hybird System, 2013, 8 : 13 -21.
  • 4Pang Guoping, Chen Lansun. A delayed SIRS epidemic model with pulse vaccination [ J ]. Science Direct Chaos, Solitons and Fractal, 2007, 34 : 1629 - 1635.
  • 5T. Zhang, Z. Teng. Pulse vaccination delayed SEIRS epidemic model with saturation incidence[ J ]. Applied Mathematical Mod- elling, 2008, 32(7) : 1403 - 1416.
  • 6Zhao Zhong, Chen Lansun, Song Xinyu. Impulsive vaccination ~f SEIR epidemic model with time delay and nonlinear incidence ~ate[ J ]. Mathematical and Computer in Simulation, 2008, 79 (3) : 500 -510.
  • 7xiang Zhongyi, Long Dan, Song Xinyu. A delayed Lotka - Volt- ~ra model birth pulse and impulsive effect at different moment on :he prey[ J]. Applied Mathematics and Computation, 2013, 219(20) : 10263 - 10270.
  • 8HE Yuying, GAO Shujing, XIE Dehui. An SIR epidemic model with time-varying pulse control schemes and saturated infectious force [J]. Applied Mathematical Modelling, 2013, 37 ( 16/17 ): 8131-8140.
  • 9XIAO Dongmei, RUAN Shigui. Global analysis of an epidemic model with non monotone incidence rate[J]. Mathematical Biosciences, 2007, 208(2):419-429.
  • 10CAI Liming,LI Xuezhi. Analysis of a SEIV epidemic model with a nonlinear incidence rate [J]. Applied Mathematics Modelling, 2009, 33(7) :2919-2926 .

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纯粹数学与应用数学
2008年 第2期

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