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Existence of Traveling Wave Solutions for Cholera Model

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  • Tianran Zhang
  • Qingming Gou
  • Xiaoli Wang

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 is defined and the formula for minimal wave speed is given. It is proved by shooting method that there exists a traveling wave solution with speed for cholera model if and only if .

Suggested Citation

  • Tianran Zhang & Qingming Gou & Xiaoli Wang, 2014. "Existence of Traveling Wave Solutions for Cholera Model," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, March.
    • Handle: RePEc:hin:jnlaaa:201094
    DOI: 10.1155/2014/201094
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