Existence of Traveling Wave Solutions for Cholera Model

Tianran Zhang, Qingming Gou, Xiaoli Wang
2014 Abstract and Applied Analysis  
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 numberR0is defined and the formula for minimal wave speedc*is given. It is proved by shooting method that there exists a
more » ... e exists a traveling wave solution with speedcfor cholera model if and only ifc≥c*.
doi:10.1155/2014/201094 fatcat:hilqgpzt45h55d2tqazxwu3zoq