Abstract
BackgroundEnsemble 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.MethodsWe 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.ResultsWe 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.ConclusionOur 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.
Highlights
The application of mathematical models to generate near real-time forecasts of the trajectory of epidemics and pandemics to guide public health interventions has been receiving increasing attention during the last decade
Using synthetic incidence curves simulated from the Gompertz model (Fig. 2), we demonstrated the functionality of the ensemble methods in 20-day ahead forecasts relative to three individual models (GLM, Richards model (RIC), GOM), a set that includes the “true model”
We found that the “true model” (GOM) outperformed all other models based on all four performance metrics it achieved a similar coverage rate of the 95% prediction intervals (PI) to that of the Ensemble Method 2, which was close to 0.95, indicating wellcalibrated models (Fig. 6)
Summary
The application of mathematical models to generate near real-time forecasts of the trajectory of epidemics and pandemics to guide public health interventions has been receiving increasing attention during the last decade. It is worth noting that the diversity of mathematical models and approaches for epidemic forecasting has been expanding, with probabilistic forecasts gaining more attention [13, 14]. Assessing prediction accuracy is a key aspect of model-based forecasting especially in the context of limited epidemiological data or the emergence of novel pathogens for which little is known about the natural course of the disease. While ensemble modeling has become a standard approach in weather forecasting systems [17, 18, 22,23,24], their application in infectious disease forecasting has only recently started to gain traction 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
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