Many vaccines don't have 100% efficacy, and diminished protection over time. The point is that if everyone has good enough protection from a vaccine, the outbre

Many vaccines don't have 100% efficacy, and diminished protection over time. The point is that if everyone has good enough protection from a vaccine, the outbreaks die down (r_0 < 1). For example, One dose of MMR vaccine is 93% effective against measles, 78% effective against mumps, and 97% effective against rubella. Two doses of MMR vaccine are 97% effective against measles and 88% effective against mumps. [1] [1] https://www.cdc.gov/vaccines/vpd/mmr/public/index.html#:~:text=One%20dose%20of%20MMR%20vaccine%20is,measles%20and%2088%25%20effective%20against%20mumps https://www.cdc.gov/vaccines/vpd/mmr/public/index.html#:~:te....