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This paper shows the outcomes of computer virus propagation (CVP) model, represented with susceptible, exposed, infected, quarantine and recovered computers (SEIRQ), classes based mathematical model using the stochastic procedures. The systematic study of the CVP based SEIRQ model represents that the equilibrium state of virus-free is stable globally with reproduction not more than one, while the viral symmetry is attractive globally. The numerical performances of the CVP based SEIRQ model are presented by using the stochastic computational framework based on the artificial neural networks (ANNs) together with the Levenberg-Marquardt backpropagation (LBMB) called as ANNs-LBMB. The learning procedures via ANNs-LBMB for solving the CVP based SEIRQ model are implemented to indorse the statics using the testing, authorization, and training. Thirteen numbers of neurons and the data selection for training 72%, testing 12% and validation 16% are selected to solve the model. For the numerical outcomes of the CVP based SEIRQ model using the ANNs-LBMB, a dataset is considered through the Adams approach. The accuracy and reliability performances of the scheme are presented by using the values of the absolute error (AE) along with the observations of state transitions (STs), regression, mean square error (MSE) and error histograms (EHs). [ABSTRACT FROM AUTHOR]