Stochastic Modeling and Inference for Type 2 Diabetes

Type 2 diabetes (T2D) is a common metabolic disorder that poses threat to human health. Blood glucose (BG) concentrations in T2D subjects can be influenced by various factors, such as stress, physical activity, and meal consumption. Obtaining personalized mathematical models for people with T2D can be beneficial for developing effective T2D management strategies, such as insulin dosing algorithms. However, fitting these models for T2D subjects can be challenging due to the limited data typically available during treatment, consisting of only Continuous Glucose Monitoring (CGM) readings and injected insulin amounts. To address this issue, we propose a stochastic jump diffusion model that incorporates the uncertainties from meal consumption behavior together with other disturbances. Additionally, we provide an inference strategy that enables us to estimate both physiological (e.g., insulin sensitivity) and behavioral (e.g., average number of meals per day) parameters using only CGM data and injected insulin amounts. We validate the proposed stochastic model and inference strategy with synthetic and clinical data, assessing their ability to estimate various parameters of the model and fit CGM data. The results demonstrate that our proposed method, along with the model, manages to estimates parameters with different interquartile range (IQR) values. Moreover, the model, in combination with the method, provide a good fit for CGM data, and demonstrates the ability to obtain estimates of unannounced meal times.