期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

具有垂直传染和脉冲接种的SIRS传染病模型的周期解 被引量：3

Periodic solutions of an SIRS epidemic model with vertical transmission and pulse vaccination
下载PDF
导出
摘要 研究了一个具有脉冲生育、脉冲接种和垂直传染的SIRS传染病模型周期解的存在性和稳定性,通过利用分岔理论,给出了超临界分岔发生的条件,得到了决定疾病流行与否的阈值,并且数值结果较好验证了理论分析. In this paper,the existence and stability of the periodic solutions of an SIRS epidemic model with birth pulse,vertical transmission and pulse vaccination are studied.By using bifurcation theory,the condition of occurrence for supercritical bifurcation is derived.The threshold for a disease to be extinct or endemic is established.Moreover,numerical results for phase portraits,periodic solutions,and bifurcation diagrams,which are illustrated with an example,are in good agreement with the theoretical analysis.
作者 郝丽杰 蒋贵荣 鹿鹏
机构地区 桂林电子科技大学数学与计算科学学院
出处 《东北师大学报（自然科学版）》 CAS CSCD 北大核心 2013年第3期35-40,共6页 Journal of Northeast Normal University(Natural Science Edition)
基金 国家自然科学基金资助项目(11162004) 广西自然科学基金资助项目(2012GXNSFAA053006) 广西研究生教育创新计划项目(YCSZ2012072)
关键词 传染病模型 脉冲 垂直传染 周期解 分岔 阈值 SIRS epidemic model pulse vertical transmission periodic solution bifurcation threshold
分类号 O175.1 [理学—基础数学]
  • 相关文献

参考文献10

  • 1ROBERTS M G, HEESTERBEEK J A P. Bluff your way in epidemic models[J]. Trends Microbiol, 1993,1~343-348.
  • 2朱玑,李维德,朱凌峰.具有脉冲出生和脉冲接种的SIR传染病模型[J].生物数学学报,2011,26(3):490-496. 被引量：9
  • 3张敬,谢守波,高文杰.一类具有时滞的SIRS传染病模型的研究[J].东北师大学报（自然科学版）,2011,43(2):10-15. 被引量：7
  • 4GAKKHAR S, NEGI K. Pulse vaccination in SIRS epidemic model with non monotonic incidence rate[J]. Chaos, Solitons and Fractals, 2008,35 : 626-638.
  • 5黄灿云,杨小光,汪训洋.一类具有时滞和双线性发生率的脉冲接种SVIR传染病模型[J].兰州理工大学学报,2012,38(4):131-135. 被引量：5
  • 6CAUGHLEY G. Analysis of vertebrate population[M]. New York:John Wiley ~Sons,1997:1-234.
  • 7I.IU Z,CHEN L. Periodic solution of a two-species competitive system with toxicant and birth pulse[J]. Chaos, Solitons and Fraetals, 2007,32 : 1703-1712.
  • 8SHUJING GAO,YUJIANG LIU,JUAN J NIETO,et al. Seasonality and mixed vaccination strategy in an epidemic model with vertical transmission[J]. Mathematics and Computers in Simulation, 2011,81:1855-1868.
  • 9ROBERTS M G. The dynamics of bovine tuberculosis in possum populations, and its eradication or control by culling or vaccination[J]. Journal of Animal Ecology, 1996,65(4) :451-464.
  • 10LAKMECHE A, ARINO O. Bifurcation of non trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment[J]. Dynamics of Continuous, Discrete and Impulsive System, 2000,7:265-287.

二级参考文献20

  • 1高淑京,滕志东.一类具饱和传染力和常数输入的SIRS脉冲接种模型研究[J].生物数学学报,2008(2):209-217. 被引量：14
  • 2MENA-LORCA, HETHCOTE H W. Dynamic models of infectious disease as regulators of population biology[J]. J Math Biol, 1992,30 : 693-716.
  • 3GAO L, HETHCOTE H W. Disease transmission models with density-dependent demographics [J].J Math Biol, 1992,30:717-731.
  • 4HALE J K. Theory of functional differential equations[M]. New York:Springer-Verlag, 1977 : 43-45.
  • 5Roberts M G, Kao R R. The dynamics of an infectious disease in a population with birth pulses[J]. Mathematical Bioscience, 1998, 149(1):23-36.
  • 6Zhou J S, Hethcote H W. Population size density dependent incidence in models for diseases without immunity[J]. Journal of Mathematical Biology, 1994, 32(8):809-834.
  • 7Roberts M G, Jowett J. An SEI model with density dependent demographics and epidemiology[J]. Journal of Mathematics Applied in Medicine and Biology, 1996, 13(4):245 257.
  • 8Diekmann O, Kretzschmar M. Patterns in the effects of infections diseases on population growth[J]. Journal of Mathematical Biology, 1991, 29(6):539-570.
  • 9d'Onofrio A. Mixed pulse vaccination strategy in epidemic model with realistically distributed infectious and latent times[J]. Applied Mathematics and Computation, 2004, 151(1):181-187.
  • 10Stone L, Shulgin B, Agur Z. Theoretical examination of the pulse vaccination policy in the SIR epidemic model[J]. Mathematical and Computer Modelling, 2000, 31(4-5):207-215.

共引文献18

同被引文献25

  • 1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
  • 2刘汉武,王荣欣,刘建新.具有性别结构的食饵-捕食者模型[J].生物数学学报,2005,20(2):179-182. 被引量：30
  • 3王拉娣,李建全.一类带有非线性传染率的SEIS传染病模型的定性分析[J].应用数学和力学,2006,27(5):591-596. 被引量：22
  • 4李学鹏,杨文生.一类具有性别结构的捕食系统[J].厦门理工学院学报,2007,15(4):50-54. 被引量：2
  • 5Donofrio A. On pulse vaccination strategy in the SIR epidemic model with vertical transmission [J]. AppliedMathematics Letters, 2005, 18(7): 729-732.
  • 6Liu X Z. Absolute stability of impulsive control systems with time delay [J]. Nonlinear Analysis, 2005, 62(3):429-453.
  • 7Gao S J, Chen L S, Teng Z D. Analysis of an SEIRS epidemic model with time delays and pulse vaccination [J].Rocky Mountain Journal of Mathematics, 2008, 38(5): 1385-1402.
  • 8Chen L S. The effect of constant and pulse vaccination on SIR epidemic model with horizontal and verticaltransmission [J]. Mathematical and Computer Modeling, 2002, 36: 1039-1057.
  • 9WANG WEN-DI,CHEN LAN-SUN. A predator-prey system with stage structure for predator[J]. Applied Mathematics andComputation, 1997,33(8) :83-91.
  • 10SAPNA DEVI. Effects of prey refuge on a ratio-dependent predator-prey model with stage-structure of prey population[J],Applied Mathematical Modelling,2013,37(6) :4337-4349.

引证文献3

二级引证文献2

东北师大学报（自然科学版）
2013年 第3期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部