A fractional differential equation model for continuous glucose monitoring data

• Main Authors: Sasikarn Sakulrang, Elvin J Moore, Surattana Sungnul, Andrea de Gaetano
• Format: Article
• Language: English
• Published: SpringerOpen 2017-05-01
• Series: Advances in Difference Equations
• Subjects: type 1 diabetes; CGM data; fractional differential equation; Brownian motion; R programs
• Online Access: http://link.springer.com/article/10.1186/s13662-017-1207-1

Abstract The main aim of this research was to test if fractional-order differential equation models could give better fits than integer-order models to continuous glucose monitoring (CGM) data from subjects with type 1 diabetes. In this research, real continuous glucose monitoring (CGM) data was analyzed by three mathematical models, namely, a deterministic first-order differential equation model, a stochastic first-order differential equation model with Brownian motion, and a deterministic fractional-order model. CGM data was analyzed to find optimal values of parameters by using ordinary least squares fitting or maximum likelihood estimation using a kernel-density approximation. Matlab and R programs have been developed for each model to find optimal values of the parameters to fit observed data and to test the usefulness of each model. The fractional-order model giving the best fit has been estimated for each subject. Although our results show that fractional-order models can give better fits to the data than integer-order models in some cases, it is clear that the models need further improvement before they can give satisfactory fits.