Stochastic model to estimate the insulin secretion using normal distribution

Glucagon Like Peptide 1 (GLP-1) exerts beneficial antidiabetic actions via effects on pancreatic β and α cells. Previous studies have focused on the improvements in β cell function, while the inhibition of α cell secretion has received less attention. The aim of this research was to quantify the relative contribution of GLP-1 induced insulin increase and glucagon decrease, on the overall glucose lowering effect of native GLP-1 infusions in a clinical setting with the help of Painleve analysis. In some cases we find that it has only the conditional Painleve property and in other cases, just the painleve property. We also obtained special solutions of Painleve analysis. In that, one of the solution (i.e) the reduction of nonlinear diffusion equation to Riccati equation was used for the insulin secretion.