The mathematical properties as positivity and positive invariance are helpful for Type 1 Diabetes mellitus (T1DM) system model to formalize the constraints of positivity on glycemia and insulinemia and the positivity of insulin infusion. Nevertheless, they are seldom used in this context. In this paper, the largest Positively Invariant Set (PIS) is computed for the open-loop system (where only a basal insulin rate is infused). Its practical interest is that hypoglycemia is prevented for any trajectory initiated inside the PIS and hypoglycemia is predicted outside the PIS. These results can be used in both open-loop usual basal-bolus therapy or to support any closed-loop control algorithm to avoid hypoglycemia.