Patents aren't the problem here, but it's an interesting thought experiment to think about what commercial terms a vaccine for AIDS or other diseases which at this point mainly affect poor, third-world people would be distributed under.

India would probably just violate the patent, claiming national security reasons, and sell it for ~production cost throughout the world. The USA might enforce a patent domestically, and it would be a rational economic choice for insurers to pay for it for many patients instead of long-term treatment if someone contracts AIDS otherwise -- if you have a 0.1% risk of contracting AIDS in a lifetime, and lifetime treatment costs $1mm, it's worthwhile to pay $100-$1000 for it.

A charity (or government) might pay for full rights to the vaccine globally, and then distribute it for the good of humanity (and to burnish their reputation), but the really out of the box thing would be for a consumer product company to distribute the vaccine cheaply, purely as a form of PR. Imagine: "Coca-Cola, the drink that is good for you. Remember, we cured AIDS."