Blood glucose concentrations of patients with type 1 diabetes mellitus are subject to very high inter- and intra-patient variability. This variability may be detrimental to the reliability of the treatment, thus resulting in potentially frequent hypo- or hyperglycemia. Model-based therapies have the potential to improve the quality of the treatment, but most of the well-accepted deterministic models of reasonable complexity are not capable of capturing intra-patient variability. The contribution of this article is to propose a method to predict individual blood glucose concentrations and the corresponding confidence intervals while accounting for inter- and intra-patient variability. For this purpose, it is proposed to construct a stochastic model by incorporating parametric uncertainty on a given continuous deterministic model and by propagating the uncertainty using the theory of the extended Kalman filter. Resulting stochastic model predictions are shown to be reliable using the FDA-approved UVa/Padova simulator and real clinical patient data. They can be used, among others, to increase safety for blood glucose control (open- as well as closed-loop), or to filter measurements.