Title: Modeling the human gut microbiome with ordinary differential equations

Abstract: In this talk, I will present some of our recent work in math biology. Specifically, I will share a mathematical model describing the growth of a gut microbiome inside and on the wall of the gut, developed based on the chemostat model with wall growth. First, I will go over the model development, existence and uniqueness, and then analysis of the steady states for the autonomous case. Then I will give a brief overview and motivation for the non-autonomous case where both the concentration and flow rate of the nutrient input are time-dependent, as well as some of the theory for the analysis. Numerical simulations will be provided to illustrate the theoretical results