Decomposition of generalized Lotka-Volterra systems and microbiome recovery

In the gut microbiome the successful administration of fecal microbiota transplantation (FMT) will convert a person's diseased microbial composition into a healthy one. We model these "healthy'' and "diseased'' microbial states as idealized ecological species, and characterize their behavior by homogenizing the properties of their constituitive microbial populations in a process called "steady state reduction'' (SSR). This method decomposes a generalized Lotka-Volterra (gLV) system of many microbial species into two-dimensional (2D) subsystems that each span a pair of steady states of the high dimensional model and obey gLV dynamics. We investigate an experimentally derived model of antibiotic-induced C. difficile infection (CDI), and study the clinically relevant transition between CDI-vulnerable (diseased) and CDI-resilient (healthy) states with the 2D subspace generated by SSR. Specifically, we investigate the ability of FMT to convert a diseased state into a healthy state, and observe that a delay in FMT administration following antibiotics may undermine its success.