I don't want to start a debate on whether vaccine mandates are a good idea or not, but assuming that a government is committed to enforcing them for all medical personnel but is concerned that they will have to fire an untenably large proportion of the essential workforce, why don't they do as the roman legions did and draw lots?

Every day/week/month, everyone who isn't vaccinated gets put into a pot, some percentage of the names are drawn, and those that are lose their jobs. Would that have close to the same effect? Is it any less fair than firing them all on the first day?

You could say that it's not safe to have unvaccinated workers around the ill, but it's also not safe for hospitals to lose significant chunks of their workforce all at once. There must be some number between 0% and 100% of loses per unit of time that allows for a minimisation of the numbers of unvaccinated healthcare workers whilst maintaining adequate staffing numbers, given an institution's capacity for hiring and training.

Just an interesting optimisation problem