Abstract

Obesity is a complicated physiological disorder that results because of the imbalance between the intake of energy and its utilization and is regulated by a complicated hormonal feedback mechanism. This paper introduces an in-depth mathematical framework to explore the mechanisms of obesity as a diet-induced condition controlled by hormonal feedback. Some of the main variables incorporated in the model are the caloric intake, energy expenditure, body fat deposition, and the regulatory functions of hormones such as insulin, leptin, and ghrelin. A system of non-linear differential equations is created to explain the interactions amongst these components, encompassing both short-term metabolic reactions and the long-term pattern of weight gain. The suggested model explains differences in the food intake, metabolic adjustment, and hormonal signaling pathways contributing to appetite, satiety, and fat storage. The stability analysis is performed to determine equilibrium points of both healthy and obese states, and the sensitivity analysis shows the most significant parameters that control the system behavior. The Simulations determine the mechanisms by which sustained high caloric nutritional intake, coupled with the dysfunctional hormonal feedback, including leptin resistance or insulin dysregulation, results in sustained weight gain and metabolic imbalance. The model also examines the intervention scenarios, such as dietary restriction and enhanced hormone sensitivity, to determine their effectiveness in turning around the obesity patterns. Findings show that early intervention and regulation of energy levels are a very big step towards returning metabolic homeostasis. The paper offers the quantitative basis of the evolution of dietinduced obesity and can be valuable in planning the specific dietary and therapeutic measures.