The more people get vaccinated, the fewer the infections.
The fewer the infections, the fewer the mutations.
The fewer the mutations, the fewer the vaccine resistant variants.
The fewer the vaccine resistant variants, the fewer the need for new vaccines.
The fewer the need for new vaccines, the fewer the need for people to get vaccinated.
Repeat.
It's hard to predict when it will happen, but infections will collapse the same way they spread, but only if people get vaccinated and retain some discipline until the collapse.
The problem with your logic is that all it took is a handful of infections in China to trigger a global pandemic. Even a "few" infections of a deadly resistant strain could prove to be problematic. That said, we do not have a full understanding of this disease yet. Its better to err on the side of caution - but not paranoia :)
Those infections in China were a problem because there was no sufficient partial immunity in the world's population. New mutations will have to overcome that partial immunity (through vaccination or prior infection), or mutate very far, which is very rare.
We do know that "far" mutations are more rare just by simple mathematics. The higher the number of mutated genes, the lower the probability for that mutation.
Wait, are you basing your argument in immunology or mathematics?
The number of mutations in each subsequent generation is not strictly linked with the ability to evade the host immune system. Most mutations are either neutral or harmful to the virus itself. All you need is a single mutation that is beneficial - which is what happened in one variant of Covid - 20I/501Y.V1, most notably a mutation in the spike - S:N501Y.
Secondly, we do know that rates of spontaneous mutations are very high in RNA viruses, or more specifically, because of the way RNA polymerase functions.
Lastly, as a nitpick, a gene is a region of DNA - which is not at play here. But I got the gist of what you wanted to say.
> The fewer the mutations, the fewer the vaccine resistant variants.
> The fewer the vaccine resistant variants, the fewer the need for new vaccines
Aren’t you committing a logical error here? There will need to be new vaccines as long as there is at least one escape variant. The “fewer the need” is really a binary 0 or 1, and you haven’t done anything to show that your “getting vaccinated and retaining some discipline until the collapse” gets us from a 1 to a 0. There’s a time component as well.
But yeah, it’s a neat story that gets shots in arms.
Mutations are happening all the time anyway, but the rate of mutation matters. This is all one big game of statistics.
Plagues end quickly all the time once conditions are no longer able to support it. Take a look at the current mouse plague in eastern Australia right now for a real world example. It's happened before but each time it collapsed as quickly as it came.
Statistically we will cross the threshold where the ecosystem is no longer favorable for the spread of covid and the plague will collapse. It will move back into the background noise just like the millions of other potential diseases that aren't currently causing a global pandemic.
The real danger are holdouts who can't or refuse to get vaccinated for whatever reason. If there's enough of them and they live close enough together to support a viable ecosystem that very well could provide a reservoir for covid to continue thriving and causing problems until they achieve herd immunity.
For one, several different variants might need to be handled with several different vaccines. Vaccines might also not work perfectly on a variant, but they might confer some protection, leading to overall less total viral particles produced, reducing the probability of an effective mutation.
The fewer the infections, the fewer the mutations.
The fewer the mutations, the fewer the vaccine resistant variants.
The fewer the vaccine resistant variants, the fewer the need for new vaccines.
The fewer the need for new vaccines, the fewer the need for people to get vaccinated.
Repeat.
It's hard to predict when it will happen, but infections will collapse the same way they spread, but only if people get vaccinated and retain some discipline until the collapse.