We model the growth of scientific literature related to COVID-19 and forecast the expected growth from 1 June 2021. Considering the significant scientific and financial efforts made by the research community to find solutions to end the COVID-19 pandemic, an unprecedented volume of scientific outputs is being produced. This questions the capacity of scientists, politicians and citizens to maintain infrastructure, digest content and take scientifically informed decisions. A crucial aspect is to make predictions to prepare for such a large corpus of scientific literature. Here we base our predictions on the Autoregressive Integrated Moving Average (ARIMA) and exponential smoothing models using the Dimensions database. This source has the particularity of including in the metadata information on the date in which papers were indexed. We present global predictions, plus predictions in three specific settings: by type of access (Open Access), by domain-specific repository (SSRN and MedRxiv) and by several research fields. We conclude by discussing our findings.@en