The key point is that if you lower the replication rate-- the number of people each person with the virus goes on to infect-- below 1, the number of active case

The key point is that if you lower the replication rate-- the number of people each person with the virus goes on to infect-- below 1, the number of active cases exponentially decays to zero. The business-as-usual replication rate of covid appears to be somewhere around 4-6, meaning that if we have universal vaccination with something like 80% efficacy, the number of active cases will exponentially decay with no other measures taken (social distancing, masks, lockdowns, quarantines etc).