A simplified estimate of the Effective Reproduction Number $R_t$ using its relation with the doubling time and application to Italian COVID-19 data

Abstract

A simplified method to compute $R_t$, the Effective Reproduction Number, is presented. The method relates the value of $R_t$ to the estimation of the doubling time performed with a local exponential fit. The condition $R_t=1$ corresponds to a growth rate equal to zero or equivalently an infinite doubling time. Different assumptions on the probability distribution of the generation time are considered. A simple analytical solution is presented in case the generation time follows a gamma distribution.