Parameter Estimation for a Jump Diffusion Model of Type 2 Diabetic Patients in the Presence of Unannounced Meals

Type 2 diabetes (T2D) has become one of the most often encountered metabolic disorders threatening the human health. Unannounced meal intake and irregular physical activity cause abrupt changes in the blood glucose concentrations. Therefore, a reliable and accurate algorithms that account for these sudden concentration changes constitute a crucial part of automated insulin pumps and dose guiders. To this end, we develop a stochastic jump diffusion model for T2D patients, reflecting the irregular frequency and uncertain amount of consumed carbohydrates. Moreover, we design a method—ombining particle Markov chain Monte Carlo and particle learning—to estimate the unknown parameters of this model, considering only continuous glucose monitoring data and amounts of injected insulin. Our approach is verified on synthetic and clinical data, demonstrating its ability to estimate the unknown parameters with a varying degree of accuracy.