Numerical results of fractional order difference system for norovirus disease with feedback neural networking

In this article, we study and analyze a novel discrete SEAIRF compartmental model in the Caputo sense to investigate the complex transmission dynamics of Norovirus, a highly infectious pathogen known for its strong environmental persistence. We carefully develop the existence and uniqueness of results using fixed-point theory and the Picard–Lindelof technique, ensuring that the system behaves regularly under biologically feasible conditions and stability. Numerical simulations based on the discrete numerical method are performed to evaluate the impact of key transmission parameters, while artificial intelligence procedures. A feedback neural network framework developed and optimized employing the Levenberg–Marquardt (LM) training method to model and predict the dynamics of the datasets. Data were subdivided into three subsets to ensure robust evaluation: 60% for model training of 300 samples, 20% for validation of 100 samples and 20% for testing of 100 samples over 788 iterations and 1000 epochs and illustrated graphically.