We introduce a multilevel functional Beta model to quantify the blood glucose levels measured by continuous glucose monitors for multiple days in study participants with type 2 diabetes mellitus. The model estimates the subject-specific marginal quantiles, quantifies the within- and between-subject variability, and produces interpretable parameters of blood glucose dynamics as a function of time from the actigraphy-estimated sleep onset. Results are validated via simulations and by studying the association between the estimated model parameters and hemoglobin A1c, the gold standard for assessing glucose control in diabetes.