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Abstract and Applied Analysis
Volume 2014, Article ID 201094, 11 pages
http://dx.doi.org/10.1155/2014/201094
Research Article

Existence of Traveling Wave Solutions for Cholera Model

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

Received 28 December 2013; Accepted 25 January 2014; Published 26 March 2014

Academic Editor: Kaifa Wang

Copyright © 2014 Tianran Zhang 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

To investigate the spreading speed of cholera, Codeço’s cholera model (2001) is developed by a reaction-diffusion model that incorporates both indirect environment-to-human and direct human-to-human transmissions and the pathogen diffusion. The two transmission incidences are supposed to be saturated with infective density and pathogen density. The basic reproduction number is defined and the formula for minimal wave speed is given. It is proved by shooting method that there exists a traveling wave solution with speed for cholera model if and only if .