Background Ensemble modeling aims to boost the forecasting performance by systematically integrating the predictive accuracy across individual models. Here we introduce a simple-yet-powerful ensemble methodology for forecasting the trajectory of dynamic growth processes that are defined by a system of non-linear differential equations with applications to infectious disease spread. Methods We propose and assess the performance of two ensemble modeling schemes with different parametric bootstrapping procedures for trajectory forecasting and uncertainty quantification. Specifically, we conduct sequential probabilistic forecasts to evaluate their forecasting performance using simple dynamical growth models with good track records including the Richards model, the generalized-logistic growth model, and the Gompertz model. We first test and verify the functionality of the method using simulated data from phenomenological models and a mechanistic transmission model. Next, the performance of the method is demonstrated using a diversity of epidemic datasets including scenario outbreak data of the Ebola Forecasting Challenge and real-world epidemic data outbreaks of including influenza, plague, Zika, and COVID-19. Results We found that the ensemble method that randomly selects a model from the set of individual models for each time point of the trajectory of the epidemic frequently outcompeted the individual models as well as an alternative ensemble method based on the weighted combination of the individual models and yields broader and more realistic uncertainty bounds for the trajectory envelope, achieving not only better coverage rate of the 95% prediction interval but also improved mean interval scores across a diversity of epidemic datasets. Conclusion Our new methodology for ensemble forecasting outcompete component models and an alternative ensemble model that differ in how the variance is evaluated for the generation of the prediction intervals of the forecasts. Supplementary Information The online version contains supplementary material available at 10.1186/s12874-021-01226-9.
【저자키워드】 Differential equations, Richards model, Model ensemble, parameter estimation, uncertainty quantification, phenomenological growth, Generalized logistic growth model, Gompertz model, Interval score, Parametric bootstrapping, 【초록키워드】 COVID-19, Influenza, Infectious disease, Forecasting, Spread, Epidemic, Coverage, Accuracy, outbreak, challenge, trajectory, dataset, Zika, Ebola, Transmission model, methodology, quantification, boost, Combination, Predictive, plague, supplementary material, growth, datasets, first test, 95% prediction interval, the epidemic, Richard, Randomly, Result, defined, evaluate, evaluated, demonstrated, interval, 【제목키워드】 Epidemic, outbreak, methodology, growth, bootstrap,