Optimizing neural networks to predict the impact of demographic heterogeneity on nonlinear fractional H1N1 transmission involving climate modeling

The impact of meteorological factors on influenza incidence in subtropical regions, such as Ontario, Canada, remains unclear. This study introduces an innovative approach to analyzing meteorological effects on nonlinear fractional influenza (H1N1) transmission using artificial intelligence techniques. Specifically, we develop multilayered auto-regressive exogenous networks (MAENs) recursively with the Levenberg–Marquardt (LM) technique, revealing significant variability in infection risk across different age groups. During a global viral outbreak, unidentified infections lead to underestimated prevalence rates and basic reproduction numbers. To better understand the spread of seasonal influenza, we construct a modeling framework based on a modified Atangana-Baleanu-Caputo (mABC) fractional-order computational process for the H1N1 model. Additionally, we analyze modifications in a non-autonomous periodic differential equation model that incorporates both climatic conditions and undocumented cases. First, we examine the qualitative properties of the proposed model, ensuring non-negativity and boundedness through the fractional-order H1N1 system computation. At the disease-free equilibrium (DFE), we conduct a local asymptotic stability (LAS) analysis and confirm stability when R0<1. Furthermore, we establish the existence of periodic solutions and prove the model’s uniform permanence. External interventions that limit interactions among age groups, enhance vaccination security, and mitigate vaccine resistance are identified as the most effective strategies for achieving therapeutic and monitoring objectives. To optimize parameter estimation, we apply the ensemble Kalman filter methodology using H1N1 data from Canada. Additionally, we employ Pontryagin’s maximum principle to validate the effectiveness of optimal control strategies. The proposed MAENs-LM approach dynamically processes data through validation, testing, and training phases, achieving the lowest mean square error (MSE) for accurate H1N1 outbreak predictions. This method effectively minimizes MSE, absolute variation, input–output correlation, error histograms, and error auto-correlation, providing a robust solution for handling the complex fractional H1N1 model.