The theoretical model of nonlinear differential equations having three variables(glucose, Insulin,  -cell mass) with thirteen parameters has been discussed in this manuscript for the first time. The model consists of a reaction-diffusion equation system that includes a nonlinear term related to enzymatic reaction kinetics. This paper provides the theoretical and numerical solutions of the nonlinear differential equation system.The homotopy perturbation method (HPM) is used to find analytical expressions of the glucose, Insulin, and  -cell mass respectively. A comparison is also provided between analytical approximation and numerical simulation. A reasonable agreement between theoretical and simulation results is founded.