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Mathematical Biosciences and Engineering

2013, Volume 10, Issue 5&6: 1335-1349. doi: 10.3934/mbe.2013.10.1335
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Dynamics of an age-of-infection cholera model

  • 1.
    Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2
  • 2.
    Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., V8W 3R4
  • 3.
    Department of Mathematics and Statistics, University of Victoria, Victoria B.C., Canada V8W 3P4
  • Received: 01 July 2012 Accepted: 29 June 2018 Published: 01 August 2013

  • MSC : Primary: 92D30; Secondary: 35B35, 35Q92.

  • A new model for the dynamics of cholera is formulated that incorporates both the infection age of infectious individuals and biological age of pathogen in the environment. The basic reproduction number is defined and proved to be a sharp threshold determining whether or not cholera dies out. Final size relations for cholera outbreaks are derived for simplified models when input and death are neglected.

    Citation: Fred Brauer, Zhisheng Shuai, P. van den Driessche. Dynamics of an age-of-infection cholera model[J]. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1335-1349. doi: 10.3934/mbe.2013.10.1335

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  • A new model for the dynamics of cholera is formulated that incorporates both the infection age of infectious individuals and biological age of pathogen in the environment. The basic reproduction number is defined and proved to be a sharp threshold determining whether or not cholera dies out. Final size relations for cholera outbreaks are derived for simplified models when input and death are neglected.


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