Abstract

Dietary intake is inherently adjustable in response to changes in meal composition, timing, and amount, which have a profound effect on metabolic regulation and overall homeostasis. This paper introduces a stochastic differential equation (SDE) framework to determine the dynamic effect of diet variability on metabolic changes, especially focusing on glucose and insulin regulation and energy balance. The expected model combines random perturbation to represent real-world reservations in dietary behavior and physiological responses using different deterministic models. The model designates metabolic homeostasis as a joined nonlinear system in which glucose intake, insulin secretion, and metabolic utilization are administered by stochastic forcing terms. These words explain variability in the intake of carbohydrates, erratic eating patterns, and external influences on lifestyles. The system is written in Ito stochastic calculus, which allows for analyzing the short-term fluctuations and long-term equilibrium behavior. Numerical reproductions are presented to assess the stability of metabolic states with varying degrees of randomness in diets. The findings suggest that moderate variability may be counterbalanced by a regulatory feedback mechanism, which ensures homeostasis within physiological ranges. However, stochastic disturbances of high intensity result in more glucose oscillations and possible destabilization of the dynamics of insulin response, which may cause a metabolic disorder, including insulin resistance. The results underscore the significance of dietary regularity in promoting metabolic stability and also illustrate the stability of biological regulatory systems when faced with moderate uncertainty. This stochastic model of human metabolism offers a more realistic depiction of human metabolic behavior than classical deterministic models, and can be applied to tailored nutritional planning, diabetes control, and predictive health analytics. In general, the work yields a solid mathematical foundation to interpret the effects of random diet fluctuations on metabolic homeostasis, which can be of excessive value to the biomedical research field and clinical nutrition interventions.