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 1st 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. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This work was supported by the Japan Agency for Medical Research and Development (grant numbers JP20fk0108535, JP21wm0125008). K.I. received funding JSPS KAKENHI (21H03490). C.P. was supported by the World-leading Innovative and Smart Education Program (1801) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan. The funders had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes All data produced in the present work are contained in the manuscript