JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (1): 116-126.doi: 10.6040/j.issn.1671-9352.0.2018.366

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Hopf bifurcation of a SIRC epidemic model with delay

LI Le-le, JIA Jian-wen*   

  1. School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, Shanxi, China
  • Published:2019-01-23

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Abstract: This article concerns a SIRC model for Influenza A with time delay. The basic reproduction number R0 is calculated. For the model without delay, we demonstrate the conditions for global stability of equilibria. And we show that the delay can only change the stability of the endemic equilibrium and lead to the existence of Hopf bifurcation. By applying the center manifold theorem, normal form theory, we also derive some explicit formulae determining the bifurcation direction and the stability of the bifurcated periodic solutions. Finally, numerical simulation is given to support our results.

Key words: SIRC model, cross-immune, delay, Hopf-bifurcation, periodic solution

CLC Number: 

  • O175.12
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