A hybrid ensemble approach: fusing ANFIS, LSTM, and LSSVM with PSO for enhanced influenza a forecasting

The rapid transmission and severe public health impacts of influenza A highlight the critical importance of accurate epidemic prediction for effective prevention and control. To address this need, this study integrates multi-source data such as weekly confirmed influenza A cases, temperature, population data, and Baidu index with spatiotemporal alignment, and develops a high-precision ensemble prediction framework by combining multiple machine learning models optimized via the Particle Swarm Optimization (PSO) algorithm, aiming to provide technical support for influenza prevention and control. Three machine learning models, namely Adaptive Network-Based Fuzzy Inference System (ANFIS), Least Squares Support Vector Machine (LSSVM), and Long Short-Term Memory (LSTM), are employed as base learners, and the PSO algorithm is applied to assign optimal weights for model fusion. After that, the predictive performance of all models is evaluated using multiple quantitative error metrics. Experimental results show that when using only influenza case time-series data, the R2 values of ANFIS, LSTM, LSSVM, and the PSO ensemble model are 0.902, 0.919, 0.905, and 0.927, with corresponding Mean Absolute Error (MAE) values of 934.68, 848.42, 919.17, and 808.69, respectively; when incorporating multi-source time-series data including temperature and Baidu index, the R2 values of the individual models and the ensemble model are 0.812, 0.824, 0.808, and 0.829, respectively, with the ensemble model consistently achieving the best performance across both prediction scenarios. This study confirms that ANFIS, LSTM, and LSSVM each possess unique strengths in influenza forecasting, and the PSO-based ensemble model effectively integrates the complementary advantages of individual base models, yielding significantly better predictive performance than any single model with improved stability and accuracy, thus providing a more reliable and practical approach for influenza outbreak prediction.