Optimizing Preventive and Treatment Strategies for Obesity Reduction: A Mathematical Modeling and Cost-Effectiveness Analysis

Numerous studies have shown that overweight and obesity significantly increase the risk of severe illnesses, including type 2 diabetes, hypertension, and knee osteoarthritis. This study aims to develop a generalized mathematical model to manage the growing prevalence of overweight and obesity. We first demonstrate that the model’s solution remains positive and bounded under specific conditions. To determine optimal intervention strategies, we apply Pontryagin’s minimum principle (PMP) to establish necessary optimality conditions. The Forward–Backward Sweeping Method (FBSM) is then used to obtain numerically optimal controls and to demonstrate their effect over a fixed time interval. The results indicate that the proposed approach effectively reduces overweight and obesity while ensuring cost-effectiveness.