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This study numerically investigates optimal intervention strategies for reducing overweight and obesity using a compartmental dynamical model with three classes: normal-weight, overweight, and obese individuals. Two time-dependent controls are considered: a preventive strategy promoting healthy lifestyles and a treatment intervention targeting obese individuals. The optimal control problem is solved using Pontryagin’s Minimum Principle and implemented numerically through the Forward–Backward Sweeping Method with a fourth-order Runge–Kutta scheme.
Simulations are performed over a 10-year horizon, assuming a constant population and initial prevalence levels consistent with reported data. Three intervention scenarios are examined: prevention only, treatment only, and a combined strategy. Results show that preventive measures significantly reduce the overweight population and indirectly lower obesity prevalence, whereas treatment directly reduces obesity but has a weaker impact on overweight individuals. The combined strategy yields the best outcomes, increasing the proportion of normal-weight individuals while reducing both overweight and obesity levels.
Optimal control profiles indicate sustained preventive effort and gradually decreasing treatment intensity over time. Overall, the numerical analysis highlights the importance of integrating preventive lifestyle campaigns with treatment programs to achieve effective long-term control of obesity.
