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.
