Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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BIFURCATION ANALYSIS OF A DELAYED EPIDEMIC MODEL WITH DIFFUSION

  • Xu, Changjin (Guizhou Key Laboratory of Economics System Simulation Guizhou College of Finance and Economics) ;
  • Liao, Maoxin (School of Mathematical Science and Computing Technology Central South University)
  • Received : 2009.01.14
  • Published : 2011.04.30
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Abstract

In this paper, a class of delayed epidemic model with diffusion is investigated. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation are also carried out to support our analytical findings. Finally, biological explanations and main conclusions are given.

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References

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