Thank you very much for your interest, Toshi. Our proposals to expand supply are consistent with scientific evidence from health practitioners, not just economists. The example of dose fractionation in the yellow fever case is meant to indicate there is precedent for dose fractionation, though the evidence that it would be effective in the case of Covid-19 comes from Moderna scientists, who have said fractional doses could be delivered without compromising efficacy. A CDC advisory panel has said boosters are not needed for healthy adults (including health care workers) and UK advisors do not recommend vaccines for early adolescents. While vaccines for these groups may nonetheless have some benefit, and we acknowledge that among health professionals there is debate, many health practitioners and economist agree that the same vaccines would have a greater health benefit as first doses for vulnerable groups including the the elderly in developing economies.