Does a critical mass of infected individuals exist after which mutations will overtake vaccination attempts?

Question

As we know, all organisms have a probability to undergo mutations when they replicate. For every infected individual with the Covid-19 their bodies are environments in which the SARS-CoV-2 may mutate beyond existing vaccines.

Therefore, as the number of infected individuals increases, there will come a point where mutations in the SARS-CoV-2 would occur faster, perhaps even concurrently in different countries, than vaccines may be developed and deployed to stamp out the virus once and for all.

So my questions are as follows: is there a critical mass* of infected people, beyond which our existing vaccine development & deployment time frames will not be able to cope with? Do we have an estimate of this number?

*I understand this is not a single, fixed number but a fuzzy, probabilistic range.

Answer 1

Epidemiological modeling
If a virus is able to change so that it renders previous vaccination inefficient, reinfecting those who were previously vaccinated, one could describe this process using epidemiological SIS model (Susceptible-Infected-Susceptible) or its modification that includes a vaccinated group (like SISV model), and indeed estimate how quick should be vaccination in order to eradicate dthe virus before everyone gets infected. One could even add a D (deaths) compartement and study whether the virus may lead to extinction of the huiman species (unlikely, since the survival rate is very high).

Real viruses
In reality we are not dealing with such a situation, since there is no reason to think that mutations make SARS-CoV-2 able to overcome the immune defenses (although they do make it more contagious and more dangerous to non-vaccinated individuals).

To clarify the issue let me outline the scenarios where viruses do escape vaccine resistance.

Influenza
Flu is known to be susceptible to vaccination, and this is a lasting vaccination. What makes this virus to come back every year is gene reshuffling, where it exchanges some of its several genes with similar viruses living in animals (the roles of some of these animals in flu outbreaks gave rise to such names as swine flu, * birs flu*, etc.). This means that every few years we are dealing with an essentially new virus (rather than a virus that has accumulated many mutations), which is not visible to the antibodies created by previously administered vaccines. In this sense, one cannot exclude a possibility of a new coronavirus causing a pandemic in a decade or so, just like the current outbreak follows similar ones due to SARS in 2002 and MERS in 2012.

HIV
HIV is know to adapt very quickly to the new antibodies, evading the immune defenses. This makes it impossible (or at least very difficult) to develop a vaccine against this virus. However, HIV is much less contagious than flu or coronavirus, since it needs to infect specific cells/tissues. In orther words, it is stopped by the barriers of the immune system other than those boosted by vaccination. Coronavirus is a much simpler virus than HIV and will never reach the same degree of sophistication via mutations.

Bacterial pathogens
Bacteria are known for routinely developing resistance to antibiotics, which has been somewhat of a hot issue in terms of antibiotic development. They however share the same weakness as HIV - being less contagious (and far more complex).

To summarize, the devil is in the details: the scenario outlined in the question is good for science fiction, but it has very low probability to be realized in real life.

Answer 2

I'm going to answer this one with a No. Outside of a simple simulation with very unrealistic constraints, we can't know the basic parameters to generate such a number. From an omniscient point of view there would be some number where this becomes inevitable, but from that point of view we could say it is inevitable or impossible right now. Some aspects to consider:

• The viral mutation rate can vary, depending on the sequence (and mutations) of the RNA-dependent RNA polymerase. That rate is presently considered slow. There is a limit (mutational load - most mutations are undesirable) to how much that rate could increase, but the limit depends on how people react to the virus, how they are treated, and so on. If one virus is in a position to infect many cells and people, it can tolerate a higher rate of errors.
• The virus can invade animal reservoirs, such as minks and cats. We do not know all the animal reservoirs, and given the scarcity of human testing, our understanding of these other reservoirs must be quite limited. We can't predict what adaptive mutation the virus might undergo to adapt to known, let alone unknown, hosts.
• RNA viruses can undergo template switching in which the 'front' of one virus is appended to the 'back' of the other. (This can be called 'recombination', though it is different from recombination in normal human cells - see this paper) The odds of this happening may depend more on where, how, and in what species the viruses interact, than on the number of people infected.
• On the plus side, there are conserved amino acid positions at which mutations will be poorly tolerated, which may be recognized by a sufficient fraction of the vaccine-induced antibodies. We can't necessarily predict whether neutral mutations presently arising will permit further mutations at residues we think are well conserved.

We really have no way of knowing whether such a point of no return has been passed already, except by an empirical approach - waiting to see whether very different Covid strains emerge from hidden animal reservoirs or rare recombination events in humans.