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This paper presents the reachability solution for a type I diabetes mellitus patient under an intensive insulin treatment. In this paper, we propose AVK (A.V. Kamyad) approach to obtain the insulin infusion rate that regulates the blood glucose level. AVK is a method where the reachability problem of a time varying state space can be converted to a minimization problem in the form of linear programming. The proposed approach can successfully regulate the blood glucose level and represents the passive insulin infusion which must be taken for the patient to reach to the normal state of blood glucose. The employed method performance is assessed in terms of its ability to reach a normoglycemic set point (70 mg/dl) in response to multiple meal disturbances resulting by food intake from the blood glucose initial sate of (180 mg/dl). The simulation results indicate the performance of the proposed AVK method on passive insulin infusion intake.