This paper addresses the problem of optimizing obesity, which has been a challenging issue in the last decade based on recent data revealed in 2024 by the World Health Organization (WHO). The current work introduces a new mathematical model of the dynamics of weight over time with embedded control parameters to optimize the number of obese, overweight, and comorbidity populations. The mathematical formulation of the model is developed under certain sufficient conditions that guarantee the positivity and boundedness of solutions over time. The model structure exhibits inherent symmetry in population group transitions, particularly around the equilibrium state, which allows the application of analytical tools such as the Routh–Hurwitz and Metzler criteria. Then, the analysis of local and global stability of the obesity-free equilibrium state is discussed based on these criteria. Based on the Pontryagin maximum principle (PMP), the deviation from the obesity-free equilibrium state is controlled. The model’s effectiveness is demonstrated through simulation using the Forward–Backward Sweeping algorithm with parameters derived from recent research in human health. Incorporating symmetry considerations in the model enhances the understanding of system behavior and supports balanced intervention strategies. Results suggest that the model can effectively inform strategies to mitigate obesity prevalence and associated health risks.
Youssef et al. (2025) studied this question.