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The Bifurcation Analysis of an SIRS Epidemic Model with StandardIncidence and Impulsive Perturbations(PDF)

《南京师大学报(自然科学版)》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2015年01期
Page:
1-
Research Field:
数学
Publishing date:

Info

Title:
The Bifurcation Analysis of an SIRS Epidemic Model with StandardIncidence and Impulsive Perturbations
Author(s):
Jiang GuirongLin JiaoLiu Suyu
School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China
Keywords:
SIRS modelstandard incidencetranscritical bifurcationflip bifurcation
PACS:
O175.1
DOI:
-
Abstract:
Birth pulse,vertical transmission,and pulse treatment are considered in an SIRS model. The dynamical behavior of an SIRS epidemic model with standard incidence is discussed by means of both theoretical and numerical ways. Firstly,by using Floquet theory,the existence and stability of the trivial solution,infection-free periodic solution,and epidemic periodic solution are proved. Secondly,the Poincare map,center manifold theorem,and bifurcation theorem are used to discuss transcritical bifurcation and flip bifurcation.The numerical results,which are illustrated with an example,are in good agreement with the theoretical analysis. Finally,biological explanations and main conclusions are given.

References:

[1] 朱矶,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(6):490-496.
[2]Zeng G Z,Chen L S. SIV-SVS epidemic models with continuous and impulsive Vaccination strategy[J]. Journal of Theoretical Biology,2011,280:108-116.
[3]马之恩,周义仓,王稳地. 传染病动力学的数学建模与研究[M]. 北京:科学出版社,2004:3-24.
[4]周艳丽,王贺桥,王美娟,等. 具有脉冲预防接种的SIQR流行病数学模型[J]. 上海理工大学学报,2007,29(1):11-16.
[5]Anderson R,May R. Infections Diseases of Human:Dynamics and Control[M]. Oxford:Oxford University Press,1991:28-38.
[6]Hua Z,Liu S,Wang H. Backward bifurcation of an epidemic model with standard incidence rate and treatment rate[J]. Nonlinear Analysis:Real World Applications,2008(9):2 302-2 312.
[7]郭中凯,王文婷,李自珍. 具有脉冲免疫接种的SEIRS传染病模型分析[J]. 南京师大学报:自然科学版,2013,36(2):20-26.
[8]Fang L L,Qi L X. The stability analysis of an SEIRS model[J]. 南京师大学报:自然科学版,2013,36(3):21-30.
[9]Rasband S N. Chaotic Dynamics of Nonlinear Systems[M]. New York:John Wiley and Sons,1990:108-110.
[10]Guckenheimer J,Holmes P. Nonlinear Oscillations,Dynamical Systems,and Bifurcations of Vector Fields,Applied Mathematical Sciences[M]. New York:Springer-Verlag,1983,42:178-180.

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Last Update: 2015-03-30