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@merridew You might find it helpful to see this as lining up the whole population, of the world, in ranks, ordered by how useful or urgent it is to immunise them.

You have enough doses for fewer ranks than are there. You have more doses of flu vaccine than of COVID.

In what order have you put your ranks?

Are the ranks identical for the 2 (and several other) vaccines?

You may care to imagine being in rank n+1
Why should you be swapped with someone in rank n?