Existence of traveling wave solutions for cholera model

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 R0 is defined and the formula for minimal wave speed c is given. It is proved by shooting method that there exists a traveling wave solution with speed c for cholera model if and only if c≥c. © 2014 Tianran Zhang et al.