一类具有标准发生率的SIRS传染病模型的无病周期解

刘苏雨; 凌琳; 蒋贵荣

您当前的位置：

首页 >

文章列表页 >

一类具有标准发生率的SIRS传染病模型的无病周期解

应用基础研究 | 更新时间：2026-09-14

- 一类具有标准发生率的SIRS传染病模型的无病周期解
- The Infection-Free Periodic Solutions of an SIRS Epidemic Model with Standard Incidence
- 中北大学学报（自然科学版） 2013年34卷第4期页码：367-371
- 作者机构：
  
  桂林电子科技大学数学与计算科学学院
- 作者简介：
- 基金信息：
  
  国家自然科学基金资助项目(11162004);广西省自然科学基金资助项目(2012GXNSFAA053006);广西省研究生教育创新计划项目(YCSZ2012072)
- DOI：
  中图分类号：
- 纸质出版：2013
- 稿件说明：
移动端阅览
刘苏雨, 凌琳, 蒋贵荣. 一类具有标准发生率的SIRS传染病模型的无病周期解[J]. 中北大学学报（自然科学版）, 2013,34(4):367-371.

刘苏雨, 凌琳, 蒋贵荣. The Infection-Free Periodic Solutions of an SIRS Epidemic Model with Standard Incidence[J]. 2013, 34(4): 367-371.
刘苏雨, 凌琳, 蒋贵荣. 一类具有标准发生率的SIRS传染病模型的无病周期解[J]. 中北大学学报（自然科学版）, 2013,34(4):367-371. DOI：

刘苏雨, 凌琳, 蒋贵荣. The Infection-Free Periodic Solutions of an SIRS Epidemic Model with Standard Incidence[J]. 2013, 34(4): 367-371. DOI：

摘要

研究了一个具有标准发生率、脉冲生育、脉冲接种和垂直传染的SIRS传染病模型的复杂动力学行为.首先构造了一个庞卡莱映射;然后利用映射的不动点及其特征值

得到了系统无病周期解的存在和稳定性的条件;接着详细讨论了系统从平凡解到无病周期-1解的跨临界分岔现象

以及从无病周期-1解到无病周期-2解的flip分岔现象;最后给出了能很好地验证理论分析的数值结果.

Abstract

The complex dynamics of an SIRS epidemic model with standard incidence

birth pulse

pulse vaccination and vertical transmission was investigated.First

a Poincaré map was constructed

the existence and stability of the infection-free periodic solution were obtained with the help of the fixed point of the map and its eigenvalues.Then transcritical bifurcation of the trivial solution and flip bifurcation of the infection-free period-1 solution of this model were discussed in detail.Finally

numerical results

which are in good agreement with the theoretical analysis

are presented.

关键词

Keywords

references

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.Zhou Yanli,Wang Heqiao,Wang Meijuan,et al.SIQR epidemical model with impulsive vaccination[J].Journal of University of Shanghai for Science andTechnology,2007,29(1):11-16.(in Chinese)

马小箭.脉冲作用下Holling-Ⅳ型捕食系统的研究[J].中北大学学报(自然科学版),2012,33(1):47-51.Ma Xiaojian.Prey-predator system with Holling-Ⅳfunctional response and impulsive effects[J].Journalof North University of China(Natural ScienceEdition),2012,33(1):47-51.(in Chinese)

Anderson R,May R.Infectious diseases of humen:dynamics and control[D].Oxford:Oxford UniversityPress,1991.

Hu Zhixing,Liu Sheng,Wang Hui.Backward bifur-cation of an epidemic model with standard incidencerate and treatment rate[J].Nonlinear Analysis:RealWorld Applications,2008,9:2302.

庞国萍,陈兰荪.具饱和传染率的脉冲免疫接种SIRS模型[J].系统科学与数学,2007,27(4):563-572.Pang Guoping,Chen Lansun.The sirs epidemic modelwith saturated contact rate and pulse vaccination[J].Journal of Systems Science and Mathematical Sci-ences,2007,27(4):563-572.(in Chinese)

Yang Y,Xiao Y.Threshold dynamics for com-part-mental epidemic models with impulses[J].NonlinearAnalysis:Real World Applications,2012,13:224-234.

Gao Shujing,Liu Yujiang,Juan J.Seasonality andmixed vaccination strategy in an epidemic model withvertical transmission[J].Mathematics and Computersin Simulation,2011,81:1855-1868.

张菊平,靳祯.具有脉冲常量接种的SIR传染病模型研究[J].中北大学学报(自然科学版),2010,31(3):205-209.Zhang Juping,Jin Zhen.Stability properties of pulseconstant vaccination strategy in SIR epidemic model[J].Journal of North University of China(NaturalScience Edition),2010,31(3):205-209.(in Chinese)

Liu Zhijun,Chen Lansun.Periodic solution of a two-species competitive system with toxicant and birthpulse[J].Chaos,Solitons and Fractals,2007,32:1703-1712.

钱临宁,陆启韶,一类自治脉冲微分方程的动力学研究[J].动力学与控制学报,2008,6(2):97-101.Qian Linning,Lu Qishao.Dynamics of a class of au-tonomous impulsive equations[J].Journal of Dynam-ics and Control,2008,6(2):97-101.(in Chinese)

Guckenheimer J,Holmes P.Nonlinear Oscillations,Dynamical Systems,and Bifurcations of Vector Fields[M].New York:Springer-Verlag,1983.

浏览量

156

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

基于低分子质量PEI的类PEG聚合物基因载体

茶叶生物炭磁性材料对水中重金属铬的超声吸附研究

鱼类自主游动时摆频与摆幅的最优组合研究

OFDM中基于DFT的自适应信道估计算法

基于递归图和MobileViT⁃AESTF的网络入侵检测模型