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In this paper, discrete-time epidemic model with a saturated incidence rate is considered. Firstly, we introduce the local stability analysis of the system by details. Next, we study the bifurcation phenomena and the sufficient condition to verify flip bifurcation and Neimark-sacker bifurcation by using bifurcation theory and the center manifold theorem. Finally, numerical simulation including bifurcation diagrams, phase portraits and Chaotic attractors is carried out by using matlab to verify theoretical results obtained.
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