The purpose of this paper is to introduce a new method based on the deep neural network method (DNN) for finding numerical solution of a novel class of stochastic biological systems. DNN utilizes the Morgan-Voyce even Lucas polynomials and \(\sinh\) function as activation functions of the deep structure. To train this neural network, we utilize the standard Brownian motion, Gauss–Legendre quadrature, and classical optimization algorithm. In the proposed method, acceptable approximate solutions are achieved by employing only a few number of the basis functions. Furthermore, we show convergence of the computational technique. Finally, the numerical technique is implemented for a stochastic biological system to illustrate the effectiveness of the presented strategy.
