The motive of this work is to provide the numerical performances of the monkeypox transmission mathematical model by using a novel deep neural network process with eleven and twenty-two neurons in the hidden layers. The purpose to provide the deep neural network stochastic process is to obtain more accurate solutions of the monkeypox transmission mathematical system. This process is enhanced by using an activation radial basis function in both layers for solving the monkeypox transmission mathematical model along with the implementation of the Bayesian regularization optimization scheme. The presentation of the mathematical dynamical model has two categories, human and rodent. The human dynamics is classified into, susceptible, exposed, infectious, clinically ill human and recovered individuals. The rodent is divided into three forms, susceptible, exposed, and infected. A dataset is presented with the Adam approach that is processed using the training, testing, and certification procedure by taking the data as 0.13, 0.12 and 0.15. The correctness is observed through the matching of the results and the statistical plots are plotted using the regression, state transition, error histograms and correlation. [ABSTRACT FROM AUTHOR]