Bifurcation Analysis Of An Epidemic Model With Delay As The Control Variable

作者: Qianqian Chi , Junjie Wei , Ying Qu

DOI:

关键词:

摘要: A SIS epidemic model proposed by Cooke et al.[2] is investigated. Using time delay as the control parameter, we investigate stability and Hopf bifurcation of analyzing distribution roots its associated characteristic equation. Then an explicit formula for determining direction bifurcating periodic solutions derived normal form theory center manifold argument. Finally, some numerical simulations are carried out supporting evidences our analytic results.

参考文章(15)
Y.-H. Wan, Nicholas D. Kazarinoff, B. D. Hassard, Theory and applications of Hopf bifurcation Cambridge University Press. ,(1981)
Zhichao Jiang, Junjie Wei, Stability and bifurcation analysis in a delayed SIR model Chaos Solitons & Fractals. ,vol. 35, pp. 609- 619 ,(2008) , 10.1016/J.CHAOS.2006.05.045
Chunrui Zhang, Junjie Wei, Stability and bifurcation analysis in a kind of business cycle model with delay Chaos Solitons & Fractals. ,vol. 22, pp. 883- 896 ,(2004) , 10.1016/J.CHAOS.2004.03.013
Xianzhang Meng, Junjie Wei, Stability and bifurcation of mutual system with time delay Chaos Solitons & Fractals. ,vol. 21, pp. 729- 740 ,(2004) , 10.1016/J.CHAOS.2003.12.050
Xiao-Qiang Zhao, Xingfu Zou, Threshold Dynamics in a Delayed SIS Epidemic Model Journal of Mathematical Analysis and Applications. ,vol. 257, pp. 282- 291 ,(2001) , 10.1006/JMAA.2000.7319
Guoping Pang, Lansun Chen, A delayed SIRS epidemic model with pulse vaccination Chaos Solitons & Fractals. ,vol. 34, pp. 1629- 1635 ,(2007) , 10.1016/J.CHAOS.2006.04.061
Weihua Jiang, Junjie Wei, Bifurcation analysis in a limit cycle oscillator with delayed feedback Chaos Solitons & Fractals. ,vol. 23, pp. 817- 831 ,(2005) , 10.1016/J.CHAOS.2004.05.028
Tailei Zhang, Junli Liu, Zhidong Teng, Bifurcation analysis of a delayed SIS epidemic model with stage structure Chaos, Solitons & Fractals. ,vol. 40, pp. 563- 576 ,(2009) , 10.1016/J.CHAOS.2007.08.004