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Abstract and Applied Analysis
Volume 2014, Article ID 369072, 8 pages
Research Article

Existence of Traveling Waves for a Delayed SIRS Epidemic Diffusion Model with Saturation Incidence Rate

1Department of Mathematics, Chizhou University, Chizhou, Anhui 247000, China
2School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China

Received 22 January 2014; Accepted 11 April 2014; Published 30 April 2014

Academic Editor: Youyu Wang

Copyright © 2014 Kai Zhou and Qi-Ru Wang. 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.


This paper is concerned with the existence of traveling waves for a delayed SIRS epidemic diffusion model with saturation incidence rate. By using the cross-iteration method and Schauder’s fixed point theorem, we reduce the existence of traveling waves to the existence of a pair of upper-lower solutions. By careful analyzsis, we derive the existence of traveling waves connecting the disease-free steady state and the endemic steady state through the establishment of the suitable upper-lower solutions.