河北工业科技2017，Vol.34Issue(3)：167-171,5.DOI:10.7535/hbgykj.2017yx03003
一类带有时滞的SIR模型的稳定性及分支分析
Analysis of stability and bifurcation of a delayed SIR model
摘要
Abstract
In order to analyze the effects of saturation incidence and time delay on the dynamics of epidemic model,a delayed SIR model with a saturated incidence rate and exponential birth is constructed.By considering the characteristic equation of the system,the stability of the endemic equilibrium is analyzed,and the critical value of the bifurcation is found.The theoretical analysis results are verified by numerical simulations.The result shows that when the delay is less than the critical value,the endemic equilibrium is locally asymptotically stable;When the delay is larger than the critical value,the endemic equilibrium is unstable and there exists a Hopf bifurcation.The results of this study can be used to explain the periodic outbreaks of infectious diseases,and guide the prevention and control of the spread of the disease.关键词
稳定性理论/SIR模型/时滞/饱和发生率/Hopf分支Key words
stability theory/SIR model/delayed/saturated incidence rate/Hopf bifurcation分类
数理科学引用本文复制引用
孔建云,刘茂省,王弯弯..一类带有时滞的SIR模型的稳定性及分支分析[J].河北工业科技,2017,34(3):167-171,5.基金项目
山西省自然科学基金(2015011009,201601D021015) （2015011009,201601D021015）
山西省留学回国人员科技活动择优资助项目 （）
山西省留学回国人员科研资助项目(2016-086) （2016-086）
