A variational model for computing the effective reproduction number of SARS-CoV-2 (preprint)

ABSTRACT

We propose a variational model for computing the effective reproduction number (ERN) of SARS-CoV-2 from the daily count of incident cases. This computation only requires the knowledge of the serial interval. The ERN estimate is made through the minimization of a functional that includes (i) the adjustment of the incidence curve using an epidemiological model, (ii) the regularity of the estimation of the ERN and, (iii) the adjustment of the initial value to an initial estimate of R_0 obtained from the initial exponential growth of the epidemic. The model does not assume any statistical distribution for the ERN and, more importantly, does not require truncating the serial interval when its distribution contains negative days. A comparative study has been carried out with the standard EpiEstim method. For a particular choice of the parameters of the variational model and of the serial interval, a good agreement has been obtained between the estimate provided by the variational model and a 7 days shifted estimate obtained by EpiEstim. This backward shift suggests that our estimate is closer to present than that of EpiEstim. We also examine how to forecast the value of the ERN and the number of infected in the short term by two different extrapolation techniques. An implementation of the model is available online at www.ipol.im/ern.