  The human gut microbiota is a complex ecosystem that affects a range of human
physiology. In order to explore the dynamics of the human gut microbiota, we
used a system of ordinary differential equations to model mathematically the
biomass of three microorganism populations: $\textit{Bacteroides
thetaiotaomicron}$, $\textit{Eubacterium rectale}$, and
$\textit{Methanobrevibacter smithii}$. Additionally, we modeled the
concentrations of relevant nutrients necessary to sustain these populations
over time. Our model highlights the interactions and the competition among
these three species. These three microorganisms were specifically chosen due to
the system's end product, butyrate, which is a short chain fatty acid that aids
in developing and maintaining the intestinal barrier in the human gut. The
basis of our mathematical model assumes the gut is structured such that
bacteria and nutrients exit the gut at a rate proportional to its volume, the
rate of volumetric flow, and the biomass or concentration of the particular
population or nutrient. We performed global sensitivity analyses using Sobol'
sensitivities to estimate the relative importance of model parameters on
simulation results.
