Yes, they have patents on some vaccines. There are a number of reasons why they hold patents, both humanitarian and sinister. The reasons one believes are true is a pretty good marker for how one feels about government and government intentions. Some would say they own the patents so that they control the vaccine so that it can be widely distributed and not exploited by greed. Others would say it is a nefarious scheme to fund their own fiefdom. The truth probably falls somewhere in between.