Modeling Metabolic State Transitions in Obesity Using a Time-Varying Lambda-Omega Framework

Obesity develops gradually over extended periods rather than emerging abruptly. Because this progression is slow and often subtle, physiological changes may remain unrecognized until excess adiposity is already established. Weight reduction is commonly framed as a simple consequence of "eating less and moving more"; however, this view overlooks the complex and adaptive nature of human metabolic regulation. During weight loss, resting metabolic rate often decreases and metabolic efficiency increases, making it progressively more difficult to maintain a caloric deficit. In contrast, during periods of overfeeding, increases in resting metabolic rate, thermogenesis, and spontaneous physical activity partially counteract excess energy intake and slow weight gain. Importantly, these compensatory responses are asymmetric, with stronger and more persistent adaptations occurring during underfeeding than during overfeeding. This asymmetry contributes to the gradual development of obesity and the biological difficulty of sustaining long-term weight loss. Here we introduce a dynamical-systems framework based on a lambda-omega model to describe metabolic regulation under lifestyle perturbations. By allowing the regulatory parameters to vary over time, the model captures progressive shifts in metabolic set-points and enables exploration of transitions between metabolic states underlying long-term weight gain and loss trajectories.