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Discrete Dynamics in Nature and Society
Volume 2011, Article ID 350892, 10 pages
Research Article

Permanence for a Delayed Nonautonomous SIR Epidemic Model with Density-Dependent Birth Rate

1College of Mathematics and Physics, Xinjiang Agricultural University, Urumqi 830052, China
2Department of Mathematics, Changji College, Changji 831100, China
3Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830054, China

Received 21 February 2011; Accepted 12 May 2011

Academic Editor: Ibrahim Yalcinkaya

Copyright © 2011 Li Yingke et al. 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.


Based on some well-known SIR models, a revised nonautonomous SIR epidemic model with distributed delay and density-dependent birth rate was considered. Applying some classical analysis techniques for ordinary differential equations and the method proposed by Wang (2002), the threshold value for the permanence and extinction of the model was obtained.