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The Scientific World Journal
Volume 2014, Article ID 409730, 14 pages
Research Article

Traveling Wave Solutions for Epidemic Cholera Model with Disease-Related Death

1School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
2College of Mathematics & Computer Science, Yangtze Normal University, Chongqing 408100, China

Received 2 January 2014; Accepted 10 March 2014; Published 27 April 2014

Academic Editors: M. Han, Z. Jin, and Y. Xia

Copyright © 2014 Tianran Zhang and Qingming Gou. 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 Codeço’s cholera model (2001), an epidemic cholera model that incorporates the pathogen diffusion and disease-related death is proposed. The formula for minimal wave speed is given. To prove the existence of traveling wave solutions, an invariant cone is constructed by upper and lower solutions and Schauder’s fixed point theorem is applied. The nonexistence of traveling wave solutions is proved by two-sided Laplace transform. However, to apply two-sided Laplace transform, the prior estimate of exponential decrease of traveling wave solutions is needed. For this aim, a new method is proposed, which can be applied to reaction-diffusion systems consisting of more than three equations.