Stochastic Gompertzian Model for Parathyroid Tumor Growth

In this paper, we study on the behavior and growth of parathyroid tumor in the human body. We investigate the change of parathyroid cancer cell with respect to time, obtained from the deterministic Gompertz model through 41 actual patients in the literature. Then we describe the stochastic Gompertz model based on deterministic Gompertz law and obtain the diffusion coefficient for our stochastic model, using the data taken from the patients. We compare the stochastic and deterministic results at the same graph. Also, we numerically solve the defined stochastic differential using the Euler-Maruyama, Milstein, stochastic Runge-Kutta, and Taylor methods. Finally, we demonstrate the effectiveness of each of these methods using graphs and error table.