Instantaneous Reproduction Number Estimation From Modelled Incidence

The time-varying reproduction number (Rt) is a critical quantity in monitoring an infectious disease outbreak. We propose a new method for estimating Rt from an infectivity profile, expressed as a generation time distribution, and a time series of probabilistic estimates of disease incidence, modelled as log-normally distributed random variables. This is a common output of disease incidence models that are based on Poisson or negative binomial regression of case counts with a logarithmic link function. The method is deterministic, computationally inexpensive and propagates inherent uncertainty in incidence estimates. We validate the method when applied to the output of two simple statistical incidence models, and using simulated data with a defined Rt and infectivity profile. This combination produces comparable outputs to the de-facto standard EpiEstim. The method can be applied to estimates of disease incidence from a wide variety of incidence models, including those derived from weekly case counts, or that account for right censoring in observed data. Author summaryIn our experience estimating the reproduction number during the COVID-19 pandemic, we found that estimating the incidence rate was a useful first step to correct for artefacts and biases in the raw count data, and to estimate the exponential growth rate. With modelled incidence estimates available, and correcting data issues, we wanted to use them to derive the time-varying reproduction number to help monitor the state of the pandemic. We present a mathematical method and supporting software to estimate Rt from modelled incidence estimates, rather than raw count data, and which is readily applicable to many incidence models.