An immuno-epidemiological model linking between-host and within-host dynamics of cholera

Beryl Musundi; Beryl Musundi

doi:10.3934/mbe.2023714

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 9: 16015-16032. doi: 10.3934/mbe.2023714

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An immuno-epidemiological model linking between-host and within-host dynamics of cholera

Beryl Musundi ^{1,2
,
,}

1.
Faculty of Mathematics, Technische Universität München, 85748 Garching, Germany
2.
Department of Mathematics, Moi University, 3900-30100 Eldoret, Kenya

Academic Editor: Xueying Wang

Received: 10 May 2023 Revised: 24 June 2023 Accepted: 10 July 2023 Published: 04 August 2023

Cholera, a severe gastrointestinal infection caused by the bacterium Vibrio cholerae, remains a major threat to public health, with a yearly estimated global burden of 2.9 million cases. Although most existing models for the disease focus on its population dynamics, the disease evolves from within-host processes to the population, making it imperative to link the multiple scales of the disease to gain better perspectives on its spread and control. In this study, we propose an immuno-epidemiological model that links the between-host and within-host dynamics of cholera. The immunological (within-host) model depicts the interaction of the cholera pathogen with the adaptive immune response. We distinguish pathogen dynamics from immune response dynamics by assigning different time scales. Through a time-scale analysis, we characterise a single infected person by their immune response. Contrary to other within-host models, this modelling approach allows for recovery through pathogen clearance after a finite time. Then, we scale up the dynamics of the infected person to construct an epidemic model, where the infected population is structured by individual immunological dynamics. We derive the basic reproduction number ($ \mathcal{R}_0 $) and analyse the stability of the equilibrium points. At the disease-free equilibrium, the disease will either be eradicated if $ \mathcal{R}_0 < 1 $ or otherwise persists. A unique endemic equilibrium exists when $ \mathcal{R}_0 > 1 $ and is locally asymptotically stable without a loss of immunity.
- cholera,
- within-host dynamics,
- between-host dynamics,
- immuno-epidemiological,
- stability analysis
Citation: Beryl Musundi. An immuno-epidemiological model linking between-host and within-host dynamics of cholera[J]. Mathematical Biosciences and Engineering, 2023, 20(9): 16015-16032. doi: 10.3934/mbe.2023714

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Abstract

Cholera, a severe gastrointestinal infection caused by the bacterium Vibrio cholerae, remains a major threat to public health, with a yearly estimated global burden of 2.9 million cases. Although most existing models for the disease focus on its population dynamics, the disease evolves from within-host processes to the population, making it imperative to link the multiple scales of the disease to gain better perspectives on its spread and control. In this study, we propose an immuno-epidemiological model that links the between-host and within-host dynamics of cholera. The immunological (within-host) model depicts the interaction of the cholera pathogen with the adaptive immune response. We distinguish pathogen dynamics from immune response dynamics by assigning different time scales. Through a time-scale analysis, we characterise a single infected person by their immune response. Contrary to other within-host models, this modelling approach allows for recovery through pathogen clearance after a finite time. Then, we scale up the dynamics of the infected person to construct an epidemic model, where the infected population is structured by individual immunological dynamics. We derive the basic reproduction number ($ \mathcal{R}_0 $) and analyse the stability of the equilibrium points. At the disease-free equilibrium, the disease will either be eradicated if $ \mathcal{R}_0 < 1 $ or otherwise persists. A unique endemic equilibrium exists when $ \mathcal{R}_0 > 1 $ and is locally asymptotically stable without a loss of immunity.

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