A Comparative Biomathematical Analysis of Fuzzy Time Series and Neural Network Models: Application to Weekly Influenza Surveillance Data from WHO FluNet

Mona Mahmoud Abo El Nasr
Department of Applied Statistics and Insurance, Faculty of Commerce, Mansoura University, Mansoura 35516, Egypt

Lamiaa A. Elboraey
Department of Statistics and Quantitative Techniques, Faculty of Business Administration, Delta University for Science and Technology, Gamasa 11152, Egypt

Elamira S. Othman
Department of Financial Sciences, Applied College, Imam Abdulrahman Bin Faisal University, Dammam 31441, Saudi Arabia

Sally A. Aladl
Department of Applied Statistics and Insurance, Faculty of Commerce, Arish University, Al-Arish 45511, Egypt

Abstract

The forecasting of seasonal influenza is a necessary component of the preparedness of the population to health risks, but the model used should be chosen so as not to lose predictive quality, interpretability, and resilience to structural regime switches. This paper provides a comparative analysis of first-order fuzzy time series (FTS) and multilayer perceptron (MLP) neural networks as models of surveillance detection of influenza on a weekly basis using laboratory-confirmed data of influenza surveillance in the United States and Australia of FluNet provided by WHO. The method used to guarantee the validity of time was a univariate lag-based model with chronological train-test splitting (pre-2019 training; post-2019 evaluation). The evaluation of performance was based on RMSE, MAE, R², and sMAPE on the same preprocessing and feature structure. Findings show that short-term autoregressive dependence prevails over weekly influenza variations because naïve persistence obtained R² of over 0.92 in both directions. The MLP resulted in small yet steady increases at high magnitude errors and better peak tracking, as compared to the first-order FTS, and structural rigidity at regime volatility. These results point at trade-offs in terms of interpretability versus nonlinear adaptability in real-time influenza surveillance forecasting.

Keywords: Influenza Surveillance, Forecasting, Fuzzy Time Series, Neural Network, Autoregression, Time-Series Epidemiology, Biomathematical Modeling