# What’s Up Doc column: Do the math: ‘Herd immunity’ not an ethical option without a COVID vaccine

Columns share an author’s personal perspective.

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Q: Wouldn’t having things go back to normal get us to herd immunity?

A: Herd immunity occurs when a large enough portion (the threshold proportion) of a community (the herd) becomes immune to a disease. Once this occurs, the disease is not able to significantly spread in terms of the number of people that become newly infected (although limited breakouts of cases may still occur), since it “runs into” enough people who are already immune to it, curtailing the spread.

Think about this like a raging forest fire, and firefighters trying to get ahead of it by starting fires to burn down certain parts of the forest so that when the spreading forest fire gets there it encounters areas of forest that are now “immune” to burning, having become “immune” by already having had their fuel burned in a fire or fires intentionally started by the firefighters. For a rapidly rampaging fire, this strategy may not be able to work since the fire might spread in many directions to “nonimmune” areas, or even “jump” over the fire breaks the firefighters have created. So, the strength and rate of the spreading fire, in this analogy akin to the infectiousness of the disease being addressed, dictate how much of the forest would need to be burned by firefighters to control it.

It is estimated that we would need 70% of the population to be immune to COVID-19 to reach herd immunity. For comparison, measles is even more contagious than the SARS-CoV-2 virus and it is estimated that 94% of the population needs to be immune to have herd immunity from that disease.

So, how can we get the threshold proportion of our population immune to SARS-Cov-2? There are two ways: vaccination or infection.

Since we don’t have a vaccine yet - I hope we will get an efficacious and safe one soon - why not allow people to get infected? Let’s do the math.

There are 330 million people in the U.S. Taking 70% as the threshold proportion yields 330 million times 70% equals 231 million people who would need to become immune via having been infected. Overall, about 2% to 3% of people infected with SARS-CoV-2 die (the mortality is higher than this in the older population and lower in younger people), and 2% of 231 million is over 4.5 million people dead, which I hope we would all agree is not a good approach!

However, since the mortality rate of COVID-19 is higher in older people and people with concomitant illnesses, what if we have everyone over 45 years old stay quarantined. (Of the 330 million population about 170 million are 44 or younger and 160 million over age 45.) So, what if we quarantine 170 million people and allow 160 million to go back to life as usual?

Unfortunately, as the virus spreads through the people under 45 it will surely “jump” to many of those over age 45. But let’s ignore this for now and just do the math.

Let’s make all very optimistic assumptions. Let’s say no one under age 20 who gets infected will die (this population does have a lower mortality rate, but unfortunately, it is NOT zero). This leaves 108 million people between the ages of 20 and 44, and we would need 70% of them to be infected which is 75.6 million people. For these people let’s say the mortality rate is 0.1% (that is 99.9% recover from the illness, and although it is really not that high, we are doing an optimistic calculation here!). 75.6 million times 0.1% equals 75,600 people.

Having done the math we can see that if we are willing to sacrifice over 75,000 of our neighbors and friends under the age of 45, and lock away the 170 million over age 45, we would achieve herd immunity (although only for the “herd” of those age 44 and younger).

Does this really seem like a reasonable option to any ethical, caring human being; having 75,000 healthy people under age 45 die and locking away the 170 million over age 45? I would hope not. But, as noted above, if we just let everyone in the country become infected, we would have at least 4.5 million dead.

I should also note that the above discussion assumes that immunity to SARS-CoV-2 will last long enough to allow us to achieve the threshold proportion and to maintain it!

So how can we achieve herd immunity in an ethical and reasonable way? The answer is vaccination. If we have a vaccine that is 70% effective (an optimistic target), and we vaccinate essentially everyone in the country (this is a very key point), we would get there! However, we know there will be too many people who will refuse the vaccine, even knowing that by doing so they are putting the lives of many of their friends and neighbors in jeopardy.

I hope that having seen the math people will now better understand what we are dealing with, and the complexity of the issue. And I hope this drives more responsible behavior from people, including getting vaccinated when a safe and effective vaccine is available!

Jeff Hersh, Ph.D., M.D., can be reached at DrHersh@juno.com.