The Infection-Free Periodic Solutions of an SIRS Epidemic Model with Standard Incidence

刘苏雨; 凌琳; 蒋贵荣

您当前的位置：

首页 >

文章列表页 >

The Infection-Free Periodic Solutions of an SIRS Epidemic Model with Standard Incidence

更新时间：2026-09-14

- The Infection-Free Periodic Solutions of an SIRS Epidemic Model with Standard Incidence
- 一类具有标准发生率的SIRS传染病模型的无病周期解
- Vol. 34, Issue 4, Pages: 367-371(2013)
- 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：
- DOI：
  CLC：
- Published：2013
- 稿件说明：
移动端阅览
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：

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.

Views

156

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

A Shock Wave Testing System for High⁃Altitude Explosion Experiments

《中北大学学报(自然科学版》》征稿简则

Study on the Removal of CO2 in Confined Space by High⁃Gravity Enhanced Potassium Hydroxide Coupled Potassium Glycinate Solution

Network Intrusion Detection Model Based on Recurrence Plot and MobileViT⁃AESTF

Study on the Ultrasonic Adsorption of Cr（Ⅵ） in Water by Tea Biochar Magnetic Materials

Related Author

No data

Related Institution

No data

⁰