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 $R_0$ 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 $c\ge c^{*}$.