Optimal Control of Blood Glucose Response in Type 2 Diabetes or Prediabetes by Physical Exercise and Meal Sequencing

Recent experimental studies show that physical exercise, meal sequencing, and their timing can significantly affect postprandial blood glucose responses in individuals with type 2 diabetes or prediabetes. This paper develops a nonlinear mathematical model that describes the effect of physical exercise and meal sequence on blood glucose response. For a prescribed set of food components within one meal and fixed aerobic and resistance exercise blocks, the problem of minimizing glucose deviation from the fasting level is formulated with a lower-glucose constraint before and after the meal. An optimal control algorithm is developed, and the main theoretical result shows that it constructs an exercise–meal sequence delivering the global minimum over the prescribed finite feasible set, whenever that set is nonempty. Illustrative examples demonstrate the proposed approach. The exercise parameters are estimated from published group-mean curves, and comparisons with separately optimized food order and exercise layout are supplemented by parameter-sensitivity tests. The results describe model-predicted responses under the specified protocol, not individual clinical effectiveness.