Insulin therapy of type 1 diabetes is essentially a case of feed-forward control in which a wrong decision can significantly affect or even harm the patient. Accordingly, the quality of the model used to predict the effect of an insulin subministration would have a paramount importance. Unfortunately, for many reasons, among them the very high interpatient and intrapatient variability and the strong influence of stochastic elements, no sufficiently reliable patienttunable models are available to predict precisely the blood glucose (BG) value development especially after meals. Against this background, attempts have been done to develop interval estimations and predictions instead of single values. This paper suggests using interval models based on physiology and describing the development of the BG in terms of transition probabilities. To this end, we use Gaussian Mixture Models (GMM) and data from real patients. The evaluation shows that the proposed approach is able to provide a good to very good prediction for time ranges of 10 to 30 minutes, both during night and day, with or without meals, while never producing a prediction which could lead to a potentially dangerous decision for the patient.