A Combined ODE Model of Carbohydrate Fermentation and Colorectal Cancer

We formulate and analyze a system of non-linear ordinary differential equations that describe key metabolic and immunological interactions between butyrate produced by fiber-fermenting gut microbiota, colorectal cancer cells and host cell populations. The model is studied both independently and in conjunction with a pre-existing carbohydrate fermentation model. The parameter space is explored through sensitivity analyses. Simulation experiments are conducted to illustrate the emergence of varying dynamical behaviour driven by butyrate availability. Our model predicts that butyrate production is driven by fiber consumption and further supported by probiotics in the case of microbial dysbiosis. It also suggests that butyrate may help in suppressing tumour growth. We also show that by adding noise with sufficiently high intensity, cancer elimination occurs almost surely in infinite time and that this threshold level of noise intensity decreases with increasing butyrate concentrations.