Predicting the time course of replacements of SARS-CoV-2 variants using relative reproduction numbers

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has continuously evolved since its introduction to the human population in 2019. Natural selection selects variants with higher effective reproduction numbers, increasing the overall transmissibility of the circulating viruses. In order to establish effective control measures for a new variant, it is crucial to know its transmissibility and replacement time course in early phases of the variant replacement. In this paper, we conduct retrospective prediction tests of the variant replacement from Alpha to Delta in England. Our method firstly estimated the relative reproduction number, the ratio of the reproduction number of a variant to that of another, from partial observations up to a given time point. Secondly, the replacement time course after the time point was predicted based on the estimates of relative reproduction number. Thirdly, the estimated relative reproduction number and the predicted time course were evaluated by being compared to those estimated using the entire observations. We found that it is possible to estimate the relative reproduction number of Delta with respect to Alpha when the frequency of Delta was more than or equal to 0.25. Using these relative reproduction numbers, predictions targeting on 1 ^st June 2021, the date when the frequency of Delta reached 0.90, had maximum absolute prediction errors of 0.015 for frequencies of Delta and 0.067 for the average relative reproduction number of circulating viruses with respect to Alpha. These results suggest that our method allows us to predict the time course of variant replacement in future from partial datasets observed in early phases of variant replacement.