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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 852698, 10 pages
http://dx.doi.org/10.1155/2013/852698
Research Article

Stationary Patterns of a Cross-Diffusion Epidemic Model

1School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China
2College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China
3Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, China
4College of Physics and Electronic Information Engineering, Wenzhou University, Wenzhou 325035, China

Received 16 September 2013; Accepted 3 October 2013

Academic Editor: Carlo Bianca

Copyright © 2013 Yongli Cai 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.

Abstract

We investigate the complex dynamics of cross-diffusion epidemic model. We first give the conditions of the local and global stability of the nonnegative constant steady states, which indicates that the basic reproduction number determines whether there is an endemic outbreak or not. Furthermore, we prove the existence and nonexistence of the positive nonconstant steady states, which guarantees the existence of the stationary patterns.