The world’s most successful vaccine has been against smallpox, which is the only human disease that has been eradicated by a vaccine. This process took several decades (!!!). Because the multi-decade roll-out of vaccines is unlikely to be repeated today, we can skip to the next example.
The measles vaccine was first available in the USA in 1963. It took roughly four years for the rate of measles to plummet.
Polio is a similar story for the United States.
Currently, it is unclear if the mRNA vaccines will ultimately eliminate the SARS-CoV-2 coronavirus in developed countries. Supposing that it does, the process would likely take years.
While the mRNA vaccines are a miracle, it is starting to look like the vaccines are only partially effective against new mutated versions of the coronavirus that are emerging. Despite high rates of vaccinations (with non-mRNA vaccines) in Seychelles, authorities are implementing social restrictions because coronavirus infections are growing among vaccinated citizens.
It is possible that countries may see better results with mRNA vaccines since those vaccines are more effective. However, the United Kingdom is a country with high rates of mRNA vaccinations. Authorities there have labelled the Indian “double mutant” b.1.617.2 variant as a ‘variant of concern’ because it is rapidly spreading despite vaccination.
While there is a possibility that multiple vaccines will eradicate the coronavirus, the more likely outcome is that new vaccine-resistant strains will emerge. Vaccines will likely offer limited cross-protection against future variants, causing mortality to be lower than what we’ve experienced. While COVID-19 has been far less problematic than past diseases that ravaged humanity, the pandemic has been a massive economic problem because every Western society has a breaking point. Even if authorities do not impose lockdowns (e.g. Sweden), citizens will impose social restrictions on themselves when the coronavirus surges in their country.