Artificial neural network scheme to solve the nonlinear influenza disease model.

• A novel integrated design is presented using the intelligent computing scheme through the designed ANNs-LMB to find the solutions of the IDNS. • The designed ANNs-LMB is accessible from the reference Adams dataset for different transmission/contact rate values (β) for the IDNS. • Closely matching of the results using the dataset of the Adams results improves the value and worth of the designed ANNs-LMB for solving the IDNS. • The presentation through relative investigations of the metrics based on regression, error histograms (EHs), mean square error (MSE) and correlation enhance the proposed ANNs-LMB for solving the IDNS. The aim of this study is to present the numerical simulations of the influenza disease nonlinear system (IDNS) using the stochastic artificial neural networks (ANNs) procedures supported with Levenberg-Marquardt backpropagation (LMB), i.e., ANNs-LMB. The IDNS is constructed with four classes, susceptible S (t), infected I (t), recovered R (t) and cross-immune people C (t), based stiff nonlinear ordinary differential system. The numerical computations have been performed through the stochastic ANNs-LMB for solving six different variations of the IDNS. The obtained numerical solutions through the stochastic ANNs-LMB for solving the IDNS have been presented using the training, verification and testing measures to reduce mean square error (MSE) from data-based reference solutions. To observed the correctness, efficiency, competence and proficiency of the designed computing paradigm ANNs-LMB, an exhaustive analysis is presented using the correlation studies, error histograms (EHs), mean squared error (MSE), regression and state transitions (STs) information. The worth and significance of ANNs-LMB is substantiated through comparisons of the outcomes admitted the good agreement from data derived results with 5–7 decimal places of accuracy for each scenario of IDNS. [ABSTRACT FROM AUTHOR]