Exploring dynamical properties of a Type 1 diabetes model using sensitivity approaches

Hannah Al Ali, Alireza Daneshkhah, Abdesslam Boutayeb, Noble Jahalamajaha Malunguza, Zindoga Mukandavire

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Abstract

The high global prevalence of diabetes, and the extortionate costs imposed on healthcare providers necessitate further research to understand different perspectives of the disease. In this paper, a mathematical model for Type 1 diabetes glucose homeostasis system was developed to better understand disease pathways. Type 1 diabetes pathological state is shown to be globally asymptomatically stable when the model threshold , and exchanges stability with the managed diabetes equilibrium state i.e. globally asymptotically stable when . Sensitivity analysis was conducted using partial rank correlation coefficient (PRCC) and Sobol method to determine influential model parameters. Sensitivity analysis was performed at different significant time points relevant to diabetes dynamics. Our sensitivity analysis was focused on the model parameters for glucose homeostasis system, at 3 to 4 hour time interval, when the system returns to homeostasis after food uptake. PRCC and Sobol method showed that insulin clearance and absorption rates were influential parameters in determining the model response variables at all time points at which sensitivity analysis was performed. PRCC method also showed the model subcutaneous bolus injection term to be important, thus identified all parameters in as influential in determining diabetes model dynamics. Sobol method complemented the sensitivity analysis by identifying relationships between parameters. Sensitivity analysis methods concurred in identifying some of the influential parameters and demonstrated that parameters which are influential remain so at every time point. The concurrence of both PRCC and Sobol methods in identifying influential parameters (in ) and their dynamic relationships highlight the importance of statistical and mathematical analytic approaches in understanding the processes modelled by the parameters in the glucose homeostasis system.
Original languageEnglish
Pages (from-to)(In press)
Number of pages30
JournalMathematics and Computers in Simulation
Volume(In press)
Early online date18 May 2022
DOIs
Publication statusE-pub ahead of print - 18 May 2022

Bibliographical note

© 2022 The Author(s). Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation (IMACS). This is an open access article under the CC BY-NC-ND license

Keywords

  • Diabetes model
  • Equilibria
  • Stability
  • Gaussian process
  • Sensitivity analysis

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