Traveling Wave Solutions for Epidemic Cholera Model with Disease-Related Death. (27th April 2014)

• Record Type: Journal Article
• Authors: Zhang, Tianran; Gou, Qingming
• Other Names: Han M. Academic Editor.; Jin Z. Academic Editor.; Xia Y. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2014(2014)
• Publication Date: 2014-04-27
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2014/409730
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : 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 c ∗ 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.