For several weeks I have been examining the current administration’s approach to fighting COVID-19, and have concluded that the underlying strategy has been that the best way to get back to normal is to allow the virus to run its course, as quickly as possible, acquire herd immunity even before a vaccine is available, and absorb the consequences.
So, I thought it might be useful to look at the concept of herd immunity, the mathematics behind it and what is necessary in order to achieve it.
Let me state at the very beginning, that I am very opposed to this strategy as being worthwhile or effective. That position is also held by the vast majority of epidemiologists, virologists and immunologists.
And yet, I expect that over the coming days we will begin to hear statements from the administration that “their experts” hold a different view, that herd immunity is a valid scientific/healthcare position. This is simply not true.
Think of the following example. Your child is ill, running a high fever. You take the child to 50 physicians for a diagnosis and treatment. 49 of them, trained in internal medicine, pediatrics or virology say that their tests, their analysis and their opinions are that the child has a bacterial infection and should be treated with antibiotics immediately. One physician, a radiologist says that this type of reaction is normal, and it will resolve by itself with no treatment at all. Should you consider these two opinions as equivalent? I do not suspect you will.
This false equivalency has been used to justify opposition to climate change science or the use of hydroxychloroquine for treating COVID-19 (which, interestingly enough did not appear on the list of medications taken by Mr. Trump during his recent battle with the virus.)
Now, to the math.
Let’s look at a classic statistical story, because it provides a good basis for understanding how one calculates herd immunity.
Consider that you are in a room with 29 other people; the group is 30 people in total. Now, suppose I offer you a bet that two people in that room will have the same birthday. Do you take the bet? Most people say “Absolutely” because they see the question from a personal perspective. There are 365 days in the year and only 30 people. There is little chance that someone in the room would have the same birthday as me, and so there is little chance that two people will have the same birthday.
Of course, I wouldn’t have even set this up if I could lose the bet. And here is why:
This is good example of how statistics work.
What is the probability that one of the other 29 people will have the same birthday as me? The probability is 29/365. Now the key is, what happens for other people. We know that you and Joe don’t have the same birthday, but what is the probability that someone else in the room has the same birthday as Joe? Now the probability is 28/365 (remember we have already tested you against Joe.). What about Mary? The probability that someone has the same birthday as Mary is now 27/365, and so on. The total probability is then the sum of each probability. Considering just the first 3 people, it is (29+28+27)/365 or 84/365.
Now, if you continue this calculation through the rest of the group, down to the very last two people (1/365), and sum up all of the probabilities, you get 465/365, and you can be extremely sure that two people in the 30 will have the same birthday.
The term “herd immunity” was coined in the early part of the 20th century to describe a phenomenon in herds of cows to resist a disease resulting in spontaneous abortion. We now use it to describe the ability of vaccines to prevent the spread of disease. Even though vaccines are seldom totally effective, and even though not all individuals get vaccinated, there is a percentage of vaccinated individuals less than 100% that will create an effective barrier to infection.
Some basic concepts behind herd immunity:
R-NAUGHT
The term r-naught, expressed “R0” refers to the infectivity of an agent (in this case a virus). A value of 1.0 means that each infected individual will pass the infection on to one other person. If the number is below 1.0, each infected individual will infect less than 1 other person. If it is greater than 1.0, each infected individual will infect more than 1 other person. Values of R0 of 1.0 or less will stem viral spread.
R0 is a conditional number based on the conditions in which the infected individual exists. For example, if the individual takes no precautions, no social distancing, no masks and no attempt to cover their mouths when they cough, the R0 will be much higher than if they did observe those self-protective actions. In order to compare the R0 of one disease to another, it is appropriate to look at what the R0 would be with no precautions in place. In that way you can compare how infectious one virus is compared to another.
For purposes of comparison, the 1918 Spanish Flu virus had an R0 of between 1.4 and 2.8. SARS and MERS had R0’s of around 1.0.
COVID-19 has an R0 identified as approximately 5.7, at least twice as high as the Spanish Flu virus. This is why it is considered “very contagious”.
LETHALITY
This is the number that expresses how many people will die as a function of how many have gotten infected. The current accepted number for COVID-19 is around 2.2%, meaning that 22 people per 1,000 infected will most likely die. As a comparison, Swine Flu (H1N1) in 2009 had a lethality rate of 0.02%, or 2 deaths per 10,000 people infected. Other viral diseases have much higher lethality rates. SARS had a death rate of 9.6%, MERS a death rate of 34.4%; Ebola had a death rate of 40.4%.
You can see that it is a combination of Lethality and R0 that creates infectivity issues. Although SARS and MERS had much higher lethality rates, their R0’s were so low that spread was far easier to contain than COVID-19.
HOW MANY PEOPLE HAVE BEEN INFECTED?
Looking to tests or positivity rates as a gauge of how many people in this country have been infected is difficult. Current estimates using testing data approximate a little over 8 million infections. We have discussed at length the shortcomings in this methodology. If you want to be tested, you need to pass a screening filter before you can get one, etc.
So, a better way to determine total infections is to calculate back from deaths. We have absorbed a total of a little over 220,000 deaths in this country, and if we use a death rate of 2.2% and include the 4-week lag in recorded deaths, we can approximate a total of around 11 million infections in this country.
HOW TO CALCULATE HERD IMMUNITY
We can now approach the statistics of herd immunity.
Consider a room of 10 people. One person enters the room who is infected with a virus. How many of those 10 people will become infected? If the R0 is 1, only one of those ten will become infected. In this case the number of infections will not increase, only one new case will be created. However, if the R0 was 2, then two of the ten will become infected and the infection will increase. The goal is to keep the infection rate to 1 or less as that will stabilize and eventually eliminate the infection.
Now, what if 2 of the 10 people in the room were immune to the disease? Now there are only 8 available people who could be infected. With an R0 of 1, less than 1 person (0.8 people) would now be infected. With an R0 of 2, 1.6 people would be infected, continuing to expand the infection in the community.
Considering an R0 of 2.0, how many people would need to be immune before the probability of a person being infected would be less than 1.0? The answer here is 5. If 5 of the 10 were immune, then the probability of one of the remaining 5 people becoming infected with an R0 of 2.0 would be 1.0, stabilizing the infection.
Therefore, the amount of population necessary to result in herd immunity for a virus with an R0 of 2.0 is 50%.
THE EQUATION!!
We want to know: What is the vaccination percentage necessary to achieve herd immunity (an infectivity rate of 1.0)?
The number can be expressed as the following: 1-(1/R0). For example, using the numbers above, if the R0 is 1.0, then the equation becomes 1-(1/1) = 0. If a virus has an R0 of 1.0, there is now need for vaccination in order to stop the spread.
If the R0 is 2.0, then the equation becomes 1-(1/2) = 0.5. If a virus has an R0 of 2.0, there needs to be an immunity of 50% in the population to reduce the infectivity to 1.0.
WHAT ABOUT COVID-19?
The R0 for COVID-19 without any protective actions taken is 5.7.
Using the equation above, we get 1-(1/5.7) = 0.825. If COVID-19 is allowed to spread without protection, we will need to have 82.5% of the population immune before the infection will stop spreading.
What about if we observe social distancing, mask wearing, and protective actions? The UK has estimated that when this is done, the R0 for COVID-19 drops to 1.4.
Now the equation yields 1-(1/1.4) = 0.29. If we observe the CDC recommendations, we will only need to have 29% of the population immune to the virus before we stop the spread of the disease.
THE EFFECTS OF HERD IMMUNITY CALCULATIONS ON TOTAL DEATHS
Looking at these calculations, we can see the expected resulting deaths.
Currently we have estimated 11 million infections in this country of 328 million people, or about 3.3%.
In the case of allowing the virus to spread unchecked, in order to achieve herd immunity as quickly as possible, we would need to infect 82.5% of the population, or 270 million people; and with a death rate of 2.2%, that would result in a total of almost 6 million deaths.
On the other hand, if we observed the recommended safety procedures, we would need to infect 29% of the population, or 95 million people and a resultant 2 million deaths. The difference here, of course is that these two scenarios are not comparable. Those who promote herd immunity by rapid infection spread, assume limited safety procedures and no extenuating circumstances other than a projected better ability to deal with those infected and a potentially lower death rate.
Those who promote safety procedures do not expect a rapid infection spread. They instead are attempting to “flatten the curve” sufficiently long as to allow a successful, effective and safe vaccine to be developed and distributed. The safety procedures will allow a limited vaccination program to be sufficiently robust as to reduce infectivity and shut down the disease. Projecting current death rates out over an additional 8 months until immunity generated by a vaccine is wide-spread, and considering a continued death rate of an average of what we have seen over the last few months, will result in an additional 200,000-300,000 deaths for a total of between 450,000 and 550,000 total deaths.
As William Haseltine, an internationally distinguished Harvard researcher and virologist said today: “Herd Immunity is another word for Mass Murder.”