Mathematical Modelling of Gut Microbial Proliferation: Implications for Precision Medicine

Abstract

The gut microbiome is known to play a crucial role in human health, and imbalances in its composition, known as dysbiosis, have been associated with various diseases, including inflammatory bowel disease (IBD), obesity, and diabetes. Precision medicine aims to tailor treatments based on individual biological information, integrating diverse omics data through mathematical modelling. This approach allows for the development of personalized therapies. Mathematical modelling of the gut microbiome provides a controlled environment for studying its dynamics and simulating long-term effects. Models can be used to explore the impacts of interventions, such as antibiotics. One commonly utilized model is the generalized Lotka-Volterra (gLV) model, which employs differential equations to describe the growth and interactions of microbial species. In this paper, we present an implementation of the gLV model in MATLAB for numerically simulating microbial population dynamics. We conduct stability analysis of the model equilibrium point by calculating the Jacobian matrix and eigenvalues. The effects of various parameters, including growth rate and interaction coefficients, are explored through numerical simulations. Additionally, we discuss studies that integrate modeling and observational approaches to gain a better understanding of the dynamics and stability of the gut microbiome. Such knowledge can contribute to the development of microbiome-targeted treatments for diseases. Future work in this field includes further refining parameter estimation methods, developing predictive models for precision medicine, and creating diagnostic tools for assessing disease risk based on microbiome profiles.