A Multi-Scale Model for Cholera Outbreaks

Beryl Musundi (), Johannes Müller and Zhilan Feng
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Beryl Musundi: Center for Mathematics, Technische Universität München, 85748 Garching, Germany
Johannes Müller: Center for Mathematics, Technische Universität München, 85748 Garching, Germany
Zhilan Feng: Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA

Mathematics, 2022, vol. 10, issue 17, 1-28

Abstract: Cholera, caused by the pathogenic Vibrio cholerae bacteria, remains a severe public health threat. Although a lot of emphasis has been placed on the population-level spread of the disease, the infection itself starts within the body. As such, we formulated a multi-scale model that explicitly connects the within-host and between-host dynamics of the disease. To model the within-host dynamics, we assigned each susceptible individual with a pathogen load that increases through the uptake of contaminated food and water (booster event). We introduced minimal and maximal times when the booster events happen and defined a time since the last booster event. We then scaled the within-host dynamics to the population where we structured the susceptible population using the two variables (pathogen load and time since the last booster event). We analyzed the pathogen load’s invariant distribution and utilized the results and time scale assumptions to reduce the dimension of the multi-scale model. The resulting model is an SIR model whose incidence function has terms derived from the multi-scale model. We finally conducted numerical simulations to investigate the long-term behavior of the SIR model. The simulations revealed parameter regions where either no cholera cases happen, where cholera is present at a low prevalence, and where a full-blown cholera epidemic takes off.

Keywords: multi-scale model; cholera; SIR; structured model; pathogen load; spectral analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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