Artificial neural network scheme to solve the nonlinear influenza disease model. (May 2022) - Sabir, Zulqurnain; Botmart, Thongchai; Asif Zahoor Raja, Muhammad; weera, Wajaree; Sadat, R.; Ali, Mohamed R.; Alsulami, Abdulaziz A.; Alghamdi, Abdullah
Highlights: 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. Abstract: 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.