Abstract

The research paper provides a coupled ordinary differential equation (ODE) system to model the dynamic interactions between diet composition, gut microbiome activity and immune response in human health. The suggested framework brings the main biological subsystems together to form a single mathematical model, which determines how nutritional input can affect the presence of microbial populations within the gut, and how microbial metabolites can affect the behaviour of the immune system. The model is meant to offer some mechanistic insights into the feedback mechanisms that coordinate metabolic balance, inflammation and general physiological stability. To reflect the dysbiosis effects, beneficial and pathogenic groups of microbes are considered independently. Immune response is also added as a state variable and is stimulated by microbial-produced signals like short-chain fatty acids and endotoxins, which inhibit or activate inflammatory pathways. These subsystems are connected by nonlinear interaction terms to enable model-to-model feedback mechanisms, including immune-mediated microbiome control and microbiomemediated immune regulation. To determine whether the system is in homeostasis or a chronic inflammatory or dysbiosis condition, stability and equilibrium analysis are done. The model shows that a healthy balance in the dietary intake encourages the diversity of the microbes and maintains the immune response, whereas a high-fat or high-sugar diet can cause an imbalance in microbial balance, which causes the prolonged activation of the immune system. Simulations also demonstrate that changes in parameters can recap clinical trends of metabolic syndrome, inflammation in the context of obesity, and intestinal immune diseases. Altogether, the presented coupled ODE framework has a theoretical basis for the interaction between diet, microbiome, and the immune system and has potential applications in personalized nutrition, preventive medicine, and computational immunology. They can be extended in the future with stochastic effects, host genetics, and multi-scale spatial dynamics to achieve more accurate predictions.