Objective: The objective of this study is to develop an efficient glucose management system based on an original control model with mixed constraints (dynamic and static constraints) to manage diets with several thresholds, using Bergman’s minimal model and Fischer’s meal models. Theoretical Framework: Personalized and healthy diets play a significant role in controlling the progression of diseases such as type 2 diabetes. Existing glucose management methods are predominantly based on dynamic mathemati- cal models and focus on diets with a single peak. However, diets with multiple thresholds better reflect realistic dietary patterns and enable more comprehen- sive glucose control. Method: The proposed model combines two key components: an objective function that minimizes the total error between the basic and generated glucose and the quantity of diet, and constraints that incorporate dynamic differential equations (Bergman’s minimal model) and static constraints representing the interval between two sensitive meals. To solve this model, the integral in the objective function is discretized using the trapezoidal rule, and dynamic con- straints are approximated using the Euler-Cauchy method. A genetic algorithm is employed to optimize the resulting static model. Several study cases, including global, partial, and one-off scenarios, are considered. Results and Discussion: Numerical simulations demonstrate that the pro- posed system effectively estimates sufficient personalized diets, grading the glycemic profile within a defined confidence zone. This approach accounts for three critical dimensions: the quantity of food, its distribution, and the intervals between successive meals. Optimal management of these parameters results in maximum dietary intake, low glucose generation, and minimal insulin secretion, enabling diabetics to maintain a near-normal lifestyle. Research Implications: This study provides a realistic and innovative frame- work for glucose management, considering the complexities of real-life dietary patterns. It highlights the significance of integrating dynamic and static con- straints in glucose control systems and contributes to the design of personalized dietary strategies for individuals with diabetes. Originality/Value: This work contributes to the literature by introducing a novel glucose management system that considers diets with multiple thresholds, enabling better control of glycemic profiles and improving the quality of life for individuals with diabetes.
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