Random chemostats with competition and different kinetics to investigate the growth of the gut microbiome

We investigate some chemostat models incorporating wall growth, competition, random fluctuations on the dilution rate, and different consumption functions (Monod and Haldane). We analyze the asymptotic behavior of the solutions of the corresponding random differential systems to establish conditions on the model parameters under which the microbes persist in the gut or disappear. Moreover, several numerical simulations are presented to support the theoretical results and illustrate their biological interpretation.