How vaccines work in my movie is they're essentially strengthened with slugcat DNA, because in universe, slugcats have a very good immune system to the point they're almost complete antiviral, antibacterial and antifungal.
And vaccines, like vaxcat the covid vaccine, he's one of the vaccines. A vaccines job in the movie and series is to teach all the cells how to fight a nasty pathogen by setting up test dummies (which represent the weakened virus part) and a photo of the viruses and a small test tube of the genetic code of the virus.