Multi-scale modeling of cholera dynamics in a spatially heterogeneous environment

Conrad Ratchford; Jin Wang; Conrad Ratchford; Jin Wang

doi:10.3934/mbe.2020051

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 2: 948-974. doi: 10.3934/mbe.2020051

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Multi-scale modeling of cholera dynamics in a spatially heterogeneous environment

Conrad Ratchford ,
Jin Wang ^,

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

Received: 27 June 2019 Accepted: 24 October 2019 Published: 07 November 2019

We propose a multi-group, multi-scale mathematical model to investigate the betweenhost and within-host dynamics of cholera. At the between-host level, we divide the total population into a number of host groups with different characteristics representing spatial heterogeneity. Our model incorporates the dual transmission pathways that include both the environment-to-human and human-to-human transmission routes. At the within-host level, our model describes the interaction among the pathogenic bacteria, viruses, and host immune response. For each host group, we couple the between-host disease transmission and within-host pathogen dynamics at different time scales. Our study thus integrates multi-scale modeling and multi-group modeling into one single framework. We describe the general modeling framework and demonstrate it through two specific and biologically important cases. We conduct detailed analysis for each case and obtain threshold results regarding the multi-scale dynamics of cholera in a spatially heterogeneous environment. In particular, we find that the between-host reproduction number is shaped by the collection of the disease risk factors from all the individual host groups. Our findings highlight the importance of a whole-population approach for cholera prevention and intervention.
- cholera dynamics,
- basic reproduction number,
- multi-group modeling,
- multi-scale modeling,
- mathematical epidemiology
Citation: Conrad Ratchford, Jin Wang. Multi-scale modeling of cholera dynamics in a spatially heterogeneous environment[J]. Mathematical Biosciences and Engineering, 2020, 17(2): 948-974. doi: 10.3934/mbe.2020051

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Abstract

We propose a multi-group, multi-scale mathematical model to investigate the betweenhost and within-host dynamics of cholera. At the between-host level, we divide the total population into a number of host groups with different characteristics representing spatial heterogeneity. Our model incorporates the dual transmission pathways that include both the environment-to-human and human-to-human transmission routes. At the within-host level, our model describes the interaction among the pathogenic bacteria, viruses, and host immune response. For each host group, we couple the between-host disease transmission and within-host pathogen dynamics at different time scales. Our study thus integrates multi-scale modeling and multi-group modeling into one single framework. We describe the general modeling framework and demonstrate it through two specific and biologically important cases. We conduct detailed analysis for each case and obtain threshold results regarding the multi-scale dynamics of cholera in a spatially heterogeneous environment. In particular, we find that the between-host reproduction number is shaped by the collection of the disease risk factors from all the individual host groups. Our findings highlight the importance of a whole-population approach for cholera prevention and intervention.

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