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A Multi-Scale Model for Cholera Outbreaks

Author

Listed:
  • Beryl Musundi

    (Center for Mathematics, Technische Universität München, 85748 Garching, Germany
    Department of Mathematics, Physics and Computing, Moi University, Eldoret P.O. Box 3900, Kenya)

  • Johannes Müller

    (Center for Mathematics, Technische Universität München, 85748 Garching, Germany
    Institute for Computational Biology, Helmholtz Center Munich, 85764 Neuherberg, Germany)

  • Zhilan Feng

    (Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA)

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.

Suggested Citation

  • Beryl Musundi & Johannes Müller & Zhilan Feng, 2022. "A Multi-Scale Model for Cholera Outbreaks," Mathematics, MDPI, vol. 10(17), pages 1-28, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3114-:d:901882
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    References listed on IDEAS

    as
    1. Cai, Li-Ming & Modnak, Chairat & Wang, Jin, 2017. "An age-structured model for cholera control with vaccination," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 127-140.
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