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

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 T0<1, and exchanges stability with the managed diabetes equilibrium state i.e. globally asymptotically stable when T0>1. 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 T0 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 T0) and their dynamic relationships highlight the importance of statistical and mathematical analytic approaches in understanding the processes modeled by the parameters in the glucose homeostasis system.