Joint estimation of the basic reproduction number and generation time parameters for infectious disease outbreaks

The basic reproduction number is a key parameter determining whether an infectious disease will persist. Its counterpart over time, the effective reproduction number, is of value in assessing in real time whether interventions have brought an outbreak under control. In this paper, we use theoretical arguments and simulation to understand the relationship between estimation of the reproduction number based on a full continuous time epidemic model and 2 other recently developed estimators. All these methods make use of "epidemic curve" data and require assumptions about the generation time distribution. The 2 simplest estimators do not require information about the-often difficult to obtain-population size. The simplest estimator is shown to require further assumptions that are rarely valid in practical settings and to produce severely biased estimates compared to the others. Furthermore, we show that in general the parameters of the generation time distribution and the reproduction number are non-identified in the early stages of an incomplete outbreak. On the basis of these results, we recommend that, wherever possible, estimation of the basic and effective reproduction numbers should be based on a well-defined epidemic model; moreover, if external information is available then it should be incorporated in a Bayesian analysis.