[1]蒋贵荣,林 娇,刘苏雨.具有标准发生率和脉冲干扰的SIRS传染病模型分岔分析[J].南京师大学报(自然科学版),2015,38(01):1.
　Jiang Guirong,Lin Jiao,Liu Suyu.The Bifurcation Analysis of an SIRS Epidemic Model with StandardIncidence and Impulsive Perturbations[J].Journal of Nanjing Normal University(Natural Science Edition),2015,38(01):1.
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具有标准发生率和脉冲干扰的SIRS传染病模型分岔分析()
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《南京师大学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]

卷:
第38卷
期数:
2015年01期
页码:
1
栏目:
数学
出版日期:
2015-06-30

文章信息/Info

Title:
The Bifurcation Analysis of an SIRS Epidemic Model with StandardIncidence and Impulsive Perturbations
作者:
蒋贵荣; 林 娇; 刘苏雨
桂林电子科技大学数学与计算科学学院,广西 桂林 541004
Author(s):
Jiang Guirong; Lin Jiao; Liu Suyu
School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China
关键词:
SIRS模型; 标准发生率; 跨临界分岔; flip分岔
Keywords:
SIRS model; standard incidence; transcritical bifurcation; flip bifurcation
分类号:
O175.1
文献标志码:
A
摘要:
本文同时考虑生育脉冲、垂直传染和脉冲治疗,建立一个带有标准发生率的SIRS传染病模型,从理论分析和数值模拟方面研究了SIRS传染病模型的动力学性质. 首先利用Floquet乘子理论,证明了系统的平凡解、无病周期解和地方病周期解的存在性和稳定性; 接着利用庞加莱映射、中心流形定理和分岔理论详细讨论了跨临界分岔和flip分岔,而且给出了能很好验证理论分析的数值结果; 最后给出了生物学的解释和主要的结论.
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.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2014-03-16.
基金项目:国家自然科学基金(11162004)、 广西自然科学基金(2012GXNSFAA053006)、广西研究生教育创新计划项目(YCSZ2014143).
通讯联系人:蒋贵荣,博士,教授,研究方向:非光滑动力系统动力学分析. E-mail:grjiang9@163.com
更新日期/Last Update: 2015-03-30