It would be interesting for you to include disease trends when no vaccine is available such as scarlet and typhoid fever. You’ll see the trends matching even though no vaccine has been available.
Also, once you hit a small number of persons infected you’ll see a drastic decline in the population. The disease basically self extinguishes. That can be the answer and not the vaccination. You can simulate this when you treat your home for pests. They don’t all have to be gone before their numbers are too low to sustain reproduction.