Developing nonlinear time-varying weighted combined prediction framework for infectious diseases: validation with respiratory infectious diseases and sexually transmitted infections

Traditional combined prediction models often face limitations in their ability to capture complex nonlinear relationships and weighting. To address these challenges, we propose a nonlinear time-varying weighted combined prediction framework that integrates deep learning algorithms, optimized activation functions, and multifractal theory. This approach results in a robust combined prediction framework. The study utilized the weekly total number of influenza cases, the daily number of confirmed cases of COVID-19, and the monthly incidence rates of HIV/AIDS and syphilis as real-world samples. Leveraging mutual information theory, combined prediction models were constructed for influenza and COVID-19 data, employing both linear and time-varying weighting methods. For HIV/AIDS and syphilis data, we applied Empirical Mode Decomposition to decompose the time series, then integrated the decomposed components via linear and time-varying weighting methods. Furthermore, multifractal theory was employed to establish an evaluation framework. The performance of individual models, linear weighted combined models, and activation function-based deep learning combined models were evaluated. This finding provides practical guidance on selecting deep learning approaches and activation functions under nonlinear time-varying weighting framework. The TCN based on Swish activation function for influenza had the best generalization and accuracy (MAE = 145.391, NMSE = 0.032, IA = 0.992). The LSTM based on Swish activation function had similar generalization and accuracy (MAE = 148.046, NMSE = 0.033, IA = 0.991). The TCN based on Swish activation function for COVID-19 had the best generalization and accuracy (MAE = 25942.744, NMSE = 0.050, IA = 0.986). The LSTM based on ELU activation function for HIV/AIDS exhibited superior predictive performance (MAE = 0.066, NMSE = 0.237, MAPE = 0.081, IA = 0.930). The LSTM based on the adjustment of ELU activation function for syphilis demonstrated superior generalization capability and accuracy (MAE = 0.096, NMSE = 0.215, MAPE = 0.037, IA = 0.931). All of them outperform linear combined prediction models. The proposed nonlinear time-varying weighted combined prediction (NTVWCP) model demonstrates improved predictive accuracy, robustness, and generalization capability compared to traditional models and conventional weighting methods.