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In this article, we develop a data assimilation procedure to predict theevolution of epidemics with data uncertainty, with application to the Covid-19pandemic. We construct a vademecum of solutions by solving the SIR epidemicmodel for a set of data neighboring the estimated real (or official) ones. Areduced basis is constructed from this vademecum through Proper OrthogonalDecomposition (POD). The reduced POD base is then applied to assimilate thepandemic data (infected, recovered, deceased) during the period in which dataare known, by a least squares procedure. The fitted curves are then used topredict the evolution of the pandemic in the next days. Validation tests forAndalusia region (Spain), Italy and Spain show accurate predictions for 7 daysthat improve as the number of assimilated data increases.

Predictive data assimilation through Reduced Order Modeling for epidemics with data uncertainty