Computing the daily reproduction number of COVID-19 by inverting the renewal equation using a variational technique

Significance Based on a signal-processing approach, we propose a method to compute the reproduction number R t , the transmission potential of an epidemic over time. R t is estimated by minimizing a functional that enforces: 1) the ability to produce an incidence curve i t corrected of the weekly periodic bias produced by the “weekend effect,” obtained from R t through a renewal equation; and 2) the regularity of R t . A good agreement is found between our R t estimate and the one provided by the currently accepted method, EpiEstim, except that our method predicts R t several days closer to present. We provide the mathematical arguments for this shift.