Neuro-computational intelligence for numerical treatment of multiple delays SEIR model of worms propagation in wireless sensor networks

•A novel design of intelligent computing paradigm using the strength/knacks of AI based procedure via two-layer structure networks of NNs-BBRT is presented to investigate the solution of the nonlinear multiple delays SEIR model for worms propagation in wireless sensor networks.•The fitness function is formulated viably using the mean square error (MSE) index for determination/analyzing the results of NNs-BBRT by utilizing the reference solutions of sundry cases of the SEIR-WSNs model through the numerical data of Adams solver.•Bayesian-regularization backpropagation networks is employed effectively for carrying learning via training, and testing sets to measure/adjust the optimization parameter of networks iteratively with epoch index to solve the SEIR-WSNs model numerically.•Efficiency, convergence, and accuracy of intelligent computing NNs-BBRT procedure to solve the nonlinear SEIR-WSNs model are endorsed by the error histogram illustrations, mean square error and regression analysis. In this study, the dynamics of a nonlinear multiple delays susceptible, exposed, infected, recovered (SEIR) model for worms propagation in wireless sensor networks (WSNs) i.e, (SEIR-WSNs) is analyzed via the design of intelligent numerical computing paradigm by exploiting the neural networks (NNs) backpropagation with the Bayesian-Regularization technique (BBRT) i.e., (NNs-BBRT). The model SEIR-WSNs is mathematically governed with ODEs system that represents the nodes as susceptible, exposed, infectious, and recovered (SEIR) nodes for the description of wireless sensor networks (WSNs). Reference outcomes are produced for the nonlinear SEIR-WSNs system using the Adams method for different scenarios based on the variation in the delays for the latent period, time taken by the antivirus to remove the worms and temporary immunization period. The reference data is used for the execution procedure of NNs-BBRT by segmenting samples into the training and testing sets to approximate the solution for nonlinear SEIR-WSNs system. The precision/accuracy and convergence of designed NNs-BBRT are validated based on the acquired accuracy through the effective fitness attainment on mean squared error (MSE), exhaustive regression analysis and sufficient error histogram illustrations.