In this paper, we discuss the identification of a physiological model describing the glucose-insulin dynamics in people with type 1 diabetes (TID). The identified model has to be applied to nonlinear model predictive control (NMPC). We propose a stochastic model of the glucose-insulin dynamics in TID. Discrete-time glucose data are provided by a continuous glucose monitor (CGM). We use maximum likelihood for parameter estimation, combined with a procedure to compute the gradient of the likelihood function. To test our identification procedure, we generate a virtual population of 10 patients using the Hovorka model and its parameter distribution. We report the estimates of the model parameters, and we use a validation dataset to evaluate the prediction errors for different prediction intervals. Whereas short-term predictions of blood glucose concentrations are consistent among patients, the accuracy of long-term predictions is more subject to inter-patient variability. The results suggest that this method has the potential to be used in NMPC algorithms.