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The formula for minimal wave speed<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:msup><mml:mi>c<\/mml:mi><mml:mo>\u2217<\/mml:mo><\/mml:msup><\/mml:mrow><\/mml:math>is given. To prove the existence of traveling wave solutions, an invariant cone is constructed by upper and lower solutions and Schauder\u2019s 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.<\/jats:p>","DOI":"10.1155\/2014\/409730","type":"journal-article","created":{"date-parts":[[2014,4,27]],"date-time":"2014-04-27T21:02:10Z","timestamp":1398632530000},"page":"1-14","source":"Crossref","is-referenced-by-count":2,"title":["Traveling Wave Solutions for Epidemic Cholera Model with Disease-Related Death"],"prefix":"10.1155","volume":"2014","author":[{"given":"Tianran","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Southwest University, Chongqing 400715, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingming","family":"Gou","sequence":"additional","affiliation":[{"name":"College of Mathematics & Computer Science, Yangtze Normal University, Chongqing 408100, 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