Will a Covid 19 vaccine get us to herd immunity: the math

The math is easy, the assumption on what percentage of the population you need to be immune to get to herd immunity is the issue:

• The usual estimates for herd immunity say that for Covid 19, you need about 60-70%% of people to be immune before herd immunity kicks in.

The first generation of vaccines is likely to be as effective as the “average” flu vaccine = roughly 50% effective but let’s suppose it is at the upper end of the efficacy of a flu vaccine which is 75%. Surveys show up to 50% of people won’t get a Covid 19 vaccine (https://www.sciencemag.org/news/2020/06/just-50-americans-plan-get-covid-19-vaccine-here-s-how-win-over-rest) As I write this roughly 3.8 million people have tested positive and perhaps as many as 10X that number have been infected and are presumably immune. Let’s make a reasonable (if depressing) estimate of how many people will be immune by the time a vaccine is introduced of 33% of the population. (Which, by the way probably means significantly more than 300,000 deaths.)

Now some 6th grade math along with that killer assumption (pun intended) that we have 50% of the population not planning on getting the vaccine:

• Immune via the vaccine: .67 (of the population assumed not already immune) *.75( effective vaccine) * .5 (% getting the vaccine) = 25.125%
• Assumed immune because they had the disease = 33%

That works out to 58.125% which is a bit shy of what most epidemiologists say is the threshold for herd immunity. But hey we could have 50% of the population infected and more than 1/2 million deaths by the time the vaccine is introduced and then we easily get to herd immunity even with 50% of the population declining to get a vaccine.

Is there any good news? Well yes, some researchers are claiming that for Covid 19, herd immunity can occur at a much lower infection rate than the 60 to 70% predicted by the usual models:

https://www.medrxiv.org/content/10.1101/2020.05.19.20104596v1.full.pdf

https://www.medrxiv.org/content/10.1101/2020.04.27.20081893v1.full.pdf

these are preprints and have not been peer reviewed. But if these papers are correct, then we would get to herd immunity even with 50% of the population declining to get the vaccine in 2021.

By the way I don’t think that everyone who wants to delay getting some of the Covid 19 vaccines in development if they are approved is an anti-vaxer. While, alas, it is probably the case that a large percentage of those saying “no” in the survey I mentioned above are anti-vaxxers, not all are. Why? Well, my medical friends who think about these kinds of questions say you can have legitimate concerns about the Moderna vaccine, because there has never been a “messenger RNA vaccine” actually used and the phase 3 trial they are conducting has only 15,000 participants getting the vaccine and may run for only only six months. This simply may not be long enough or large enough to reveal if it has any unusual (low frequency) problems. This is why, as I understand it, in the early days, when it is primarily health care workers and first responders getting the Moderna vaccine (if it is approved), they will all be tracked for any issues that they may develop. (This is what is usually called a “phase 4” trial.) This tracking will let us see if this new vaccine technology is as safe as the phase 3 showed. (For what it is worth, I would get it when it becomes available to the general public, because I am in such a high risk group.) Again please keep in mind that the Oxford vaccine uses a different technology (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4994731/) that has a longer track record, so I don’t think there is any rational reason not to get the Oxford vaccine if it is approved as soon as possible, but again I’m not a doctor.

Still, I do have to end this post by noting that William Haseltine, a well known and respected virologist, in an op-ed recently in CNN (https://www.cnn.com/2020/07/13/opinions/herd-immunity-covid-19-uncomfortable-reality-haseltine/index.html) pointed out that for corona viruses like Covid 19, getting to herd immunity isn’t likely the end of the problem for such a deadly disease. Why? Because immunity seems to be very short lived for corona type viruses. However, what he didn’t note is that since Covid 19 isn’t mutating very rapidly, keeping up herd immunity may “only” mean that we may all need a booster shot every six months or so – forever.

Added: As far as I can tell, if this paper is correct (and I have no reason to believe it is not), then the hope of long lived immunity from a Covid 19 vaccine is a pipe dream:

https://www.medrxiv.org/content/10.1101/2020.07.09.20148429v1