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One common way to test for diabetes is the Oral Glucose Tolerance Test or OGTT. Most common methods for the analysis of the data on this test are wasteful of much of the information contained therein. We propose to model blood glucose…

In this paper, we propose a model of the dynamics of the blood glucose level during an Oral Glucose Tolerance Test (OGTT). This dynamic includes the action of insulin and glucagon in the glucose homeostasis process as the reaction of an…

OGTT is a common test, frequently used to diagnose insulin resistance or diabetes, in which a patient's blood sugar is measured at various times over the course of a few hours. Recent developments in the study of OGTT results have framed it…

In the Oral Glucose Tolerance Test (OGTT), a patient, after an overnight fast ingests a load of glucose. Then measurements of glucose concentration are taken every 30 minutes during two hours. The test is used to aid diagnosis of diabetes,…

A common test for the diagnosis of type 2 diabetes is the Oral Glucose Tolerance Test (OGTT). Recent developments in the study of OGTT tests have framed it as a Bayesian inverse problem. These data analysis advances promise great…

In this paper, we build a new, simple, and interpretable mathematical model to estimate and forecast physiology related to the human glucose-insulin system, constrained by available data. By constructing a simple yet flexible model class…

Mathematical models of glucose, insulin, and pancreatic $\beta$-cell mass dynamics are essential for understanding the physiological basis of type 2 diabetes. This paper investigates the Topp model's discrete-time dynamics to represent…

In the context of time-series forecasting, we propose a LSTM-based recurrent neural network architecture and loss function that enhance the stability of the predictions. In particular, the loss function penalizes the model, not only on the…

Diabetes Mellitus is a metabolic disorder which may result in severe and potentially fatal complications if not well-treated and monitored. In this study, a quantitative analysis of the data collected using CGM (Continuous Glucose…

The human insulin-glucose metabolism is a time-varying process, which is partly caused by the changing insulin sensitivity of the body. This insulin sensitivity follows a circadian rhythm and its effects should be anticipated by any…

A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…

Modeling the dynamics of probability distributions from time-dependent data samples is a fundamental problem in many fields, including digital health. The goal is to analyze how the distribution of a biomarker, such as glucose, changes over…

Diabetes mellitus is a disease that affects to hundreds of millions of people worldwide. Maintaining a good control of the disease is critical to avoid severe long-term complications. In recent years, several artificial pancreas systems…

In this work we develop an ordinary differential equations (ODE) model of physiological regulation of glycemia in type 1 diabetes mellitus (T1DM) patients in response to meals and intravenous insulin infusion. Unlike for the majority of…

The mathematical modelling of biological systems has historically followed one of two approaches: comprehensive and minimal. In comprehensive models, the involved biological pathways are modelled independently, then brought together as an…

A variety of oscillations are observed in pancreatic islets.We establish a model, incorporating two oscillatory systems of different time scales: One is the well-known bursting model in pancreatic beta-cells and the other is the…

We develop a new model of insulin-glucose dynamics for forecasting blood glucose in type 1 diabetics. We augment an existing biomedical model by introducing time-varying dynamics driven by a machine learning sequence model. Our model…

Reliable optimal control is challenging when the dynamics of a nonlinear system are unknown and only infrequent, noisy output measurements are available. This work addresses this setting of limited sensing by formulating a Bayesian prior…

The insulin sensitivity (IS) of the human body changes with a circadian rhythm. This adds to the time-varying feature of the glucose metabolism process and places challenges on the blood glucose (BG) control of patients with Type 1 Diabetes…

For most stochastic dynamical systems, variables which are tightly regulated tend to respond slowly to external changes. This idea is often discussed for applicable systems, within a linear response regime, through the Fluctuation…