Stochasticity influences the efficacy of simulated bacteriotherapies

We consider a stochastic bistable two-species generalized Lotka-Volterra model of the microbiome and use it as a testbed to analytically and numerically explore the effects of direct (e.g. fecal microbiota transplantation) and indirect (e.g. changes in diet) bacteriotherapies. Two types of noise are included in this model, representing the immigration of bacteria into and within the gut (additive noise) and variations in growth rate associated with the spatially inhomogeneous distribution of resources (multiplicative noise). The efficacy of a bacteriotherapy is determined by comparing the mean first-passage times (the average time required for the system to transition from one basin of attraction to the other) with and without the intervention. We use concepts from transition path theory to investigate how the role of noise affects these bacteriotherapies, and probe the relationship between the deterministic and stochastic systems by comparing isocommittor surfaces of the stochastic system to the separatrix of the deterministic system.