Epidemiological Forecasting with Model Reduction of Compartmental Models. Application to the COVID-19 Pandemic

SIMPLE SUMMARY: Using tools from the reduced order modeling of parametric ODEs and PDEs, including a new positivity-preserving greedy reduced basis method, we present a novel forecasting method for predicting the propagation of an epidemic. The method takes a collection of highly detailed compartmental models (with different initial conditions, initial times, epidemiological parameters and numerous compartments) and learns a model with few compartments which best fits the available health data and which is used to provide the forecasts. We illustrate the promising potential of the approach to the spread of the current COVID-19 pandemic in the case of the Paris region during the period from March to November 2020, in which two epidemic waves took place. ABSTRACT: We propose a forecasting method for predicting epidemiological health series on a two-week horizon at regional and interregional resolution. The approach is based on the model order reduction of parametric compartmental models and is designed to accommodate small amounts of sanitary data. The efficiency of the method is shown in the case of the prediction of the number of infected people and people removed from the collected data, either due to death or recovery, during the two pandemic waves of COVID-19 in France, which took place approximately between February and November 2020. Numerical results illustrate the promising potential of the approach.