A plan that lets every country have Affordable Vaccines (a free* idea)

The two problems that currently exist are:

1) Only some countries have vaccine factories - and they tend to provide for their own people first

2) Poorer countries typically cannot afford vaccines

The solutions I propose are:

1) The UN runs all vaccine production

2) Companies that create vaccines must charge the same rate regardless of who wishes to purchase it. And that price must be a percentage of each countries GDP per capita - or some other indicator of affordability, like purchasing power parity (PPP). So someone in Zambia might pay $1 for their vaccine, whereas someone in the USA needs to pay $200.

The problem is not that poor countries cannot afford vaccines, but more that prosperous countries get them far too cheap (relatively).