References
- NHS, 2014 (accessed 11th December 2015). NHS Choices – Health A-Z – Diabetes. Available at http://www.nhs.uk/Conditions/Diabetes/Pages/Diabetes.aspx
- R.N. Bergman, Y.Z. Ider, C.R. Bowden, and C. Cobelli , Quantitative estimation of insulin sensitivity, Am. J. Phys. 236 (1979), pp. 667–677.
- E. Ackerman, J.W. Rosevear, and W.F. McGucking, A mathematical model of the glucose tolerance test, Phys. Med. Biol. 9 (1964), pp. 203–213.
- V.W. Bolie, Coefficients of normal blood glucose regulation, J. Appl. Physiol. 16 (1961), pp. 783–788.
- A. De Gaetano and O. Arino, Mathematical modelling of the intravenous glucose tolerance test, J. Math. Biol. 40 (2000), pp. 136–168.
- J. Yang, S. Tang, and A. Robert, The regulatory system for diabetes mellitus: Modeling rates of glucose infusions and insulin injections, Commun. Nonlinear Sci. Numer. Simul. 37 (2016), pp. 305–325.
- J. Li, Y. Kuang, and C. Mason, Modeling the glucose-insulin regulatory system and ultradian insulin secretory oscillations with two time delays, J. Theor. Biol. 242 (2006), pp. 722–735.
- B. Topp, K. Promislow, G. Devries, R.M Miura, and D.T Finegood, A model of β-cell mass, insulin, and glucose, J. Theor. Biol. 206 (2000), pp. 605–619.
- H. Wang, J. Li, and Y. Kuang, Mathematical modeling and qualitative analysis of insulin therapies, Math. Biosci. 210 (2007), pp. 17–33.
- H. Wang, J. Li, and Y. Kuang, Enhanced modelling of the glucose-insulin system and its applications in insulin therapies, J. Biol. Dyn. 3(1) (2009), pp. 22–38.
- M. Lombarte, M. Lupo, L. Fina Brenda, G. Campetelli, A.R. Buzalaf Marilia, M. Basualdo, and A. Rigalli, In vivo measurement of the rate constant of liver handling of glucose and glucose uptake by insulin-dependent tissues, using a mathematical model for glucose homeostasis in diabetic rats, J. Theor. Biol. 439 (2018), pp. 205–215.
- B. Huard, J. Easton, and M. Angelova, Investigation of stability in a two-delay model of ultradian oscillations in glucose-insulin regulation, Commun. Nonlinear Sci. Numer. Simul. 26 (1–3) (2015), pp. 211–222.
- I.M. Tolic, E. Mosekilde, and J. Sturis, Modeling the insulin-glucose feedback system: The significance of pulsatile insulin secretion, J. Theor. Biol. 7(2000), pp. 361–375.
- K. Engelborghs, V. Lemaire, J. Bélair, and D. Roose, Numerical bifurcation analysis of delay differential equations arising from physiological modeling, J. Math. Biol. 42(4) (2001), pp. 361–385.
- M. Pitchaimani, P. Krishnapriya, and C. Monica, Mathematical modeling of intravenous glucose tolerance test model with two discrete delays, J. Biol. Syst. 23(4) (2015), pp. 1550031.
- J.P. Maianti, A. McFedries, Z.H. Foda, R.E. Kleiner, X.Q. Du, M.A. Leissring, Wei-Jen Tang, M.J.Charron, M.A. Seeliger, A. Saghatelian, and D.R. Liu, Anti-diabetic activity of insulin-degrading enzyme inhibitors mediated by multiple hormones, Nature 511 (7507) (2014), pp. 94–98.
- B. Huard, A. Bridgewater, and M. Angelova, Mathematical investigation of diabetically impaired ultradian oscillations in the glucose-insulin regulation, J. Theor. Biol. 418 (2017), pp. 66–76.
- N. Chitnis, J.M. Hyman, and J.M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, B. Math. Biol. 70 (2008), pp. 1272–1296.
- L. Arriola and J. Hyman, Lecture notes, forward and adjoint sensitivity analysis: with applications in dynamical systems, Linear Algebra Optim. Math. Theor. Biol. Inst., 2005, Summer
- Chinese Diabetes Society, Guideline for the prevention and treatment of type 2 diabetes mellitus in China (2020 edition). Chin. J. Diabetes Mellitus 13 (4) (2021), pp. 320
- J.A. Mayfield and R.D. White, Insulin therapy for type 2 diabetes: Rescue, augmentation, and replacement of β-cell function, Am. Fam. Physician 70 (2004), pp. 489–500.
- I.B. Hirsch, Type 1 diabetes mellitus and the use of flexible insulin regimens, Am. Fam. Physician 60 (1999), pp. 2343–2352. 2355–2356.