During infectious disease outbreaks, the time-dependent reproduction number ([Formula: see text]) can be estimated to monitor pathogen transmission. In previous work, we developed a simulation-based method for estimating [Formula: see text] from temporally aggregated disease incidence data (e.g. weekly case reports). While that approach is straightforward to use, it assumes implicitly that all cases are reported and the computation can be slow when applied to large datasets. In this article, we extend our previous approach and develop a computationally efficient simulation-based method for estimating [Formula: see text] in real-time accounting for both temporal aggregation of incidence data and under-reporting (with a fixed reporting probability per case). Using simulated data, we show that failing to consider stochastic under-reporting can lead to inappropriately precise estimates, including scenarios in which the true [Formula: see text] value lies outside inferred credible intervals more often than expected. We then apply our approach to data from the 2018 to 2020 Ebola outbreak in the Democratic Republic of the Congo (DRC), again exploring the effects of case under-reporting. Finally, we show how our method can be extended to account for temporal variations in reporting. Given information about the level of case reporting, our framework can be used to estimate [Formula: see text] during future outbreaks with under-reported and temporally aggregated case data.This article is part of the theme issue 'Uncertainty quantification for healthcare and biological systems (Part 2)'.