Existence of traveling wave solutions for cholera model. (English) Zbl 1470.92376

Summary: To investigate the spreading speed of cholera, C. T. Codeço’s cholera model [“Endemic and epidemic dynamics of cholera: the role of the aquatic reservoir”, BMC Infect. Dis. 1, No. 1, 1–14 (2001; doi:10.1186/1471-2334-1-1)] 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 \(c \geq c^*\).


92D30 Epidemiology
Full Text: DOI


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