The last decade has seen a surge of interest in understanding the functional relationships between the elements that make up the diverse ecology of the gut microbiome. This ecological web includes bacteria, viruses, and microbes that enter, populate and leave living hosts. They affect metabolism and stimulate the immune system, directly or indirectly modulating most physiological functions.
Specific animal models are being explored in the context of their particular roles in this ecological web. For example, consider the importance of the insect gut microbiota as an invisible third faction in the chemical arms race that has given rise to a large portion of Earth's terrestrial diversity. Mathematical modeling has recently begun to play a role in our understanding of the functioning of the microbiome and how the microbiome is affected by the outside world.
In this paper, we present a mathematical model that describes the spatial dynamics of several competing bacterial populations along with a toxin that inhibits the growth of one of bacterial populations and is degraded by the other bacteria. The model consists of a system of four non-linear partial differential equations describing the interactions of the bacteria as they flow through the digestive tract. The model simulations and analysis give insight into possible mechanisms to explore in future laboratory experiments.
