Modeling cholera dynamics at multiple scales: environmental evolution, between-host transmission, and within-host interaction

Conrad Ratchford; Jin Wang; Conrad Ratchford; Jin Wang

doi:10.3934/mbe.2019037

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 2: 782-812. doi: 10.3934/mbe.2019037

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Research article

Modeling cholera dynamics at multiple scales: environmental evolution, between-host transmission, and within-host interaction

Conrad Ratchford ,
Jin Wang ^,

Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA

Received: 30 August 2018 Accepted: 23 November 2018 Published: 15 January 2019

Cholera is an acute intestinal illness caused by infection with the bacterium Vibrio cholerae. The dynamics of the disease transmission are governed by human-human, environmenthuman, and within-human sub-dynamics. A multi-scale model is presented to incorporate all three of these dynamical components. The model is divided into three subsystems where the dynamics are analyzed according to their respective time scales. For each subsystem, we conduct a careful equilibrium analysis, with a focus on the disease threshold characterized by the basic reproduction number. Finally, the three subsystems are combined to discuss the dynamical properties of the full system.
- cholera dynamics,
- multi-scale modeling,
- basic reproduction number
Citation: Conrad Ratchford, Jin Wang. Modeling cholera dynamics at multiple scales: environmental evolution, between-host transmission, and within-host interaction[J]. Mathematical Biosciences and Engineering, 2019, 16(2): 782-812. doi: 10.3934/mbe.2019037

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Abstract

Cholera is an acute intestinal illness caused by infection with the bacterium Vibrio cholerae. The dynamics of the disease transmission are governed by human-human, environmenthuman, and within-human sub-dynamics. A multi-scale model is presented to incorporate all three of these dynamical components. The model is divided into three subsystems where the dynamics are analyzed according to their respective time scales. For each subsystem, we conduct a careful equilibrium analysis, with a focus on the disease threshold characterized by the basic reproduction number. Finally, the three subsystems are combined to discuss the dynamical properties of the full system.

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