Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (6): 1415-1425.

• Articles • Previous Articles     Next Articles

Bifurcation Analysis of a SIRS Epidemic Model with Saturating Contact Rate and Vertical Transmission

 LING Lin, LIU Su-Yu, JIANG Gui-Rong   

  1. School of Mathematics and Computational Science, Guilin University of Electronic Techology, Guilin 541004
  • Received:2013-10-13 Revised:2014-11-27 Online:2014-12-25 Published:2014-12-25
  • Supported by:

    国家自然科学基金(11162004)、广西自然科学基金(2012GXNSFAA053006)和广西研究生教育创新计划项目(YCSZ2012072)资助.

Abstract:

The complex dynamics of a SIRS epidemic model with saturate incidence rate, birth pulse, pulse vaccination and vertical transmission was studied. First, a Poincar\'e map was formulated, 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, 
supercritical bifurcation and flip bifurcation were discussed in detail. Finally, numerical results, which are in good agreement with the theoretical analysis, were presented.

Key words: SIRS epidemic model, Saturating contact rate, Transcritical bifurcation, Supercritical bifurcation, Flip bifurcation

CLC Number: 

  • 34A37
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