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具有垂直传染的SEIR疾病模型的Hopf分支分析 被引量：1

The Hopf Bifurcation of an Seir Eqidemic Model with Vertical Transmission
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摘要 研究了一类既具有垂直传染又具有水平传染的SEIR时滞模型的稳定性,证明了当时间延迟到达或穿过临界值时,系统的正平衡点附近出现了一族周期解,得到了平衡点附近出现周期解的充分条件. We study a delay differential for infectious disease that spreads in the host population through both horizontal and vertical transmission.Proving the stability of the positive equilibrium change when the delay cross a sequence of critical values.Getting the sufficient condition of Hopf bifurcation nearby the positive equilibrium.
作者 于莉琦 李文学
机构地区 黑龙江东方学院数学教研室 哈尔滨工业大学(威海)
出处 《生物数学学报》 2015年第4期753-757,共5页 Journal of Biomathematics
关键词 传染病模型 时间延迟 稳定性 Time delay Hopf bifurcation Stability
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献7

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  • 2付景超,井元伟,张中华,张嗣瀛.具垂直传染和连续预防接种的SIRS传染病模型的研究[J].生物数学学报,2008,23(2):273-278. 被引量：33
  • 3陈军杰.若干具有非线性传染力的传染病模型的稳定性分析[J].生物数学学报,2005,20(3):286-296. 被引量：26
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  • 5Michael Y. Li,Hal L. Smith,Liancheng Wang.Global dynamics an SEIR epidemic model with vertical transmission. SIAM Journal on Applied Mathematics . 2001
  • 6Xianzhang Meng,Junjie Wei.??Stability and bifurcation of mutual system with time delay(J)Chaos, Solitons and Fractals . 2004 (3)
  • 7Yongli Song,Maoan Han,Junjie Wei.Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays[J]. Physica D: Nonlinear Phenomena . 2004 (3)

二级参考文献19

  • 1陈军杰.若干具有非线性传染力的传染病模型的稳定性分析[J].生物数学学报,2005,20(3):286-296. 被引量：26
  • 2杨建雅,张凤琴.一类具有垂直传染的SIR传染病模型[J].生物数学学报,2006,21(3):341-344. 被引量：22
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共引文献57

同被引文献6

  • 1Michael Y Li, Hal L. Smith and Liancheng Wang. GlobalDynamics of An Seir Eqidemic Model with Vertical Transmis- sion. SIAMJ. App Math,2001,62 : 158 - 169.
  • 2Feichtinger G, Forst C V, Piccardi C. A nonlinear Dynamical Model for the Dynastic Cycle [ J ]. Chaos Solitons & Fractals, 1996,7(2) : 257 -271.
  • 3Wei Junjie, Li Michael Y. Global Existence of Periodic solu- tion in A Tri - neuron Model with Delays [ J ]. Physical D, 201M,198(1 ) :106 -119.
  • 4Rebecca V, Culashaw, Ruan Shigui. A Delay - differential Equation Model of HIV Infection of CIM T- cells[ J]. Math- ematical Biosciences ,2000,165 ( 1 ) :27 - 39.
  • 5Song Yongli, Han Maoan, Wei Junjie. Stability and Hopf Bi- furcation Analysis on a Simplified BAM Neural Network with Delays [ J ]. Physical D, 2005,200 ( 1 ) : 185 - 204.
  • 6Ding Xiaohuan, Li Wenxue. Local Hopf bifurcation and glob- al existence of periodic solutions in a kind of physiological system[ J]. Nonlinear Analysis : Real World .

引证文献1

生物数学学报
2015年 第4期

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