Fig. 4

Models of blood glucose regulation by insulin. A Steady-state value of blood glucose as a function of glucose uptake according to Eq.  11 for different rates of insulin secretion (upper) and degradation (lower). Dashed lines correspond to the unregulated system. B Steady-state value of blood glucose as a function of glucose consumption according to model 11 for different rates of insulin secretion (upper) and degradation (lower). C Diagram of a supply-driven model of insulin regulation including the paracrine effect of insulin on its own secretion. D Steady-state value of blood glucose as a function of glucose uptake according to model 12 for different rates of insulin secretion (left) and degradation (right). Parameter values: \(\delta _G=0.6\) and \(\mu =0.1\). Scenarios of insulin secretion: \(s_S=1,2,4\) and \(d_S=2\). Scenarios of insulin degradation: \(d_S=1,2,4\) and \(s_S=2\). Dashed lines in A and B correspond to the unregulated model (\(s_S=0\), \(d_S=0\), and \(\mu =0\)). Parameters have been arbitrarily chosen to illustrate the dynamics of the models