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Discrete Dynamics in Nature and Society
Volume 2013, Article ID 705601, 8 pages
Research Article

Bifurcation and Chaotic Behavior of a Discrete-Time SIS Model

Department of Mathematics and Sciences, Hebei Institute of Architecture and Civil Engineering, Zhangjiakou, Hebei 075000, China

Received 5 January 2013; Accepted 8 April 2013

Academic Editor: Qingdu Li

Copyright © 2013 Junhong Li and Ning Cui. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The discrete-time epidemic model is investigated, which is obtained using the Euler method. It is verified that there exist some dynamical behaviors in this model, such as transcritical bifurcation, flip bifurcation, Hopf bifurcation, and chaos. The numerical simulations, including bifurcation diagrams and computation of Lyapunov exponents, not only show the consistence with the theoretical analysis but also exhibit the rich and complex dynamical behaviors.