Simultaneous estimation of the effective reproduction number and the time series of daily infections: Application to Covid-19

The time-varying effective reproduction number is an important parameter for communication and policy decisions during an epidemic. In this paper, we present new statistical methods for estimating the reproduction number based on the popular model of \citet{cori2013new} which defines the effective reproduction number based on self-exciting dynamics of new infections. Such a model is conceptually simple and less susceptible to misspecifications than more complicated multi-compartment models. However, statistical inference is challenging, and the previous literature has either relied on proxy data and/or a two-step approach in which the number of infections is first estimated. In contrast, we present a coherent Bayesian method that approximates the joint posterior of daily new infections and reproduction numbers using a novel Markov chain Monte Carlo (MCMC) algorithm. Comparing our method to the state-of-the-art three-step estimation procedure of \citet{huisman2022estimation}, both using daily confirmed cases from Switzerland in the Covid-19 epidemic and simulated data, we find that our method is more accurate in terms of point estimates and uncertainty quantification, especially near the beginning and end of an observation period.