A Polynomial Linear Regression Approach to Estimate Sensitive Parameters in the Novel Double Diabetes Model

Main Article Content

Rashida Hussain
Asma Arbab
Salahuddin -
Mohammad Munir
Nasreen Kausar
Asghar Ali


Sensitivity analysis characterizes the changes in the model outputs due to the changes in the model parameters. In this article, we estimate the most sensitive parameters in the Novel Double Diabetes Model (NDDM) through the polynomial linear regression approach; this way we develop a direct relation between the sensitivity analysis and the paramter estimation. The NDDM has more than seventeen parameters, and estimating them simultanously is difficult. We select the most commonly used five parameters in the glucose-insulin dynamics for the sensitivity analysis. The model outputs-glucose concentrations in the plasma and the subcutaneous compartments are sensitive to the selected parameters whereas the insulin concentrations in the plasma and the subcutaneous compartment are sensitive only to the insulin transfer rate from the subcutaneous to the plasma compartment. System sensitivity of the model for the selected parameters is also in agreement with the individual sensitivities of the parameters. Consequently, we estimate the parameters which are more sensitive by the polynomial linear regression approach.

Article Details


  1. E. Ackerman, L.C. Gatewood, J.W. Rosevear, G.D. Molnar, Model studies of blood-glucose regulation. J. Bull Math Biophys. 27 (1) (1965), 21-37.
  2. A. Ali, M. Munir, R. Hussain, S. Aziz, Mathematical Analysis of TB Model, J. Sci. Arts. 20 (1) (2020), 119-128.
  3. R.N. Bergman, Y.Z. Ider, C.R. Bowden, C. Cobelli, Quantitative estimation of insulin sensitivity., Amer. J. Physiol., Endocrinol. Metab. 236 (1979), E667.
  4. W. Boutayeb, M. Lamlili, A. Boutayeb, M. Derouich, The Impact of Obesity on Predisposed People to Type 2 Diabetes: Mathematical Model. In: OrtuËœno F., Rojas I. (eds) Bioinformatics and Biomedical Engineering. IWBBIO 2015. Lecture Notes in Computer Science, vol 9043. Springer, Cham. 2015. https://doi.org/10.1007/978-3-319-16483-0 59
  5. G. Eigner, B. Kurtan, I.J. Rudas, C.C. Kong, L.A. Kovacs, Examination of a novel double diabetes model, in: 2015 IEEE 13th International Symposium on Applied Machine Intelligence and Informatics (SAMI), IEEE, Herl'any, Slovakia, 2015: pp. 41-46.
  6. R. Hovorka, F. Shojaee-Moradie, P.V. Carroll, L.J. Chassin, I.J. Gowrie, N. C. Jackson, R.S. Tudor, A. M. Umpleby, R.H. Jones, Partitioning Glucose Distribution/Transport, Disposal, and Endogenous Production during IVGTT. Amer. J. Physiol., Endocrinol. Metab. 282 (5) (2002), 992-1007.
  7. F. Kappel, M. Munir, A New Approach to Optimal Design Problems, Proc. Int. Conf. Nonlinear Anal. Optim. October 6 - 10, 2008, Budva (Montenegro).
  8. F. Kappel, M. Munir, Generalized sensitivity functions for multiple output systems, J. Inverse Ill-Posed Probl. 25 (4) (2017), 499-519.
  9. J. Li, Y. Kuang, C. C. Mason, Modeling the glucose-insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays, J. Theor. Biol. 242(3) (2006), 722-735.
  10. J. Li, Y. Kuang, Analysis of a model of the glucose-insulin regulatory system with two delays. SIAM J. Appl. Math. 67 (3) (2007), 757-776.
  11. M. Munir, Sensitivity and Generalized Sensitivity Studies of the SIR and SEIR Models of Computer Virus. Proc. Pakistan Acad. Sci. A. Phys. Comput. Sci. 54 (2) (2017), 167-178.
  12. M. Munir, A. Ali, and R. Hussain, An Improved Mathematical Model of Solute Kinetic During Hemodialysis, Punjab Univ. J. Math. 50 (1) (2018), 55-66.
  13. M. Munir, Generalized sensitivity analysis of the minimal model of the intravenous glucose tolerance test, Math. Biosci. 300 (2018), 14-26.
  14. M. Munir, On the Concept of Off-Diagonal Generalized Sensitivity Functions and Their Relations to the Parameter Estimates and Correlation. Punjab Univ. J. Math. 51 (1) (2019), 61-77.
  15. W.R. Puckett, Dynamic Modeling of Diabetes Mellitus, PhD Diss., Department of Chemical Engineering, The University of Wisconsin-Madision USA, 1992.
  16. J. T. Sorensen, A physiologic model of glucose metabolism in man and its use to design and assess improved insulin therapies for diabetes PhD diss., Massachusetts Institute of Technology USA, 1985.
  17. J. Sturis, K.S. Polonsky, E. Mosekild, E. Van Cauter. Computer model for mechanisms underlying ultradian oscillations of insulin and glucose, Amer. J. Physiol., Endocrinol. Metab., 260 (5) (1991) E801-9.
  18. W.U. Zimei, Mathematical models with delays for glucose-insulin regulation and applications in artificial pancreas, PhD diss., National University of Singapore, 2013.