Estimated reproduction ratios in the SIR model

The aim of this article is to understand the extreme variability in estimates of the reproduction ratio R₀ observed in practice. For expository purposes, we consider a discrete-time, stochastic version of the susceptible-infected-recovered model and introduce different approximate maximum likelihood estimators of R₀. We carefully discuss the properties of these estimators and illustrate, by a Monte Carlo study, the widths of confidence intervals for R₀.