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A theoretical analysis of the control of plasma glucose levels in diabetic individuals is undertaken using a simple mathematical model of the dynamics of glucose and insulin interaction in the blood system. Mathematical optimization techniques are applied to the mathematical model to derive insulin infusion programs for the control of blood levels in diabetic individuals. Based on the results of the mathematical optimization, a semiclosed-loop algorithm is proposed for continuous insulin delivery to diabetic patients. The algorithm is based on three hourly plasma glucose samples. A theoretical evaluation of the effectiveness of this algorithm shows that it is superior to two existing algorithms in controlling hyperglycemia. A glucose infusion term representing the effect of glucose intake resulting from a meal is introduced into the model equations. Various insulin programs for the control of plasma glucose levels following a meal are then assessed. The theoretical results suggest that the most effective short-term control is achieved by an insulin infusion program which incorporates an injection to coincide with the meal.