First, let’s define what herd immunity is. I think this is necessary because I have witnessed people arguing on social media that we can’t reach herd immunity until a vaccine is developed. This is incorrect. I suppose people have this impression because the topic of herd immunity is something that is normally discussed in connection with vaccines.

Herd immunity can either be naturally or “unnaturally” acquired. Herd immunity is acquired when the rate of new infections begins to decline due to a sufficient percentage of the population achieving immunity. At this point, exponential increase in new infections stops. This can be naturally acquired by a percentage of the population being infected with the actual virus. It does not require a vaccine.

The question becomes, what percentage of the population must be infected before herd immunity is realized? This is called the Herd Immunity Threshold (HIT).

Mathematically determining the HIT for a given virus is extremely complicated. It’s a mathematically complex calculation that’s based on compartmentalized SEIR models which are based on differential calculus.

The simplest model is to assume that the virus has a equal propensity to infect all people the same, and that all people have an equal probability of being exposed to the virus, being infected, and infecting other people. A simple model treats the population homogenously and divides people into four categories depending on their current state: Susceptible, Exposed, Infectious, and Recovered. As the model progresses over time by employing differential calculus, people are shuffled sequentially from the susceptible bucket, to the exposed bucket, to the infectious bucket, to the recovered bucket.

As the recovered bucket grows over time, the rate of transmission decreases because it becomes less probable to be exposed to an infected person. This causes the effective reproduction number (Re) to continually drop. When this value reaches 1, herd immunity is said to be achieved and the rate of new infections begins to decline and the virus “burns” out in the population.

As stated, the simplest models treat the population equally, meaning there is no difference between Sally or John In terms of being infected or spreading the virus to others. If this assumption is made, the HIT can be calculated as:

HIT = 1 – 1/Ro

Ro is the basic reproduction number for the virus, which is a measure of the average number of people the average person infects once infected. For the virus that causes COVID-19 (SARS-COV-2), Ro is somewhere between 2.5 – 3.0. This puts the herd immunity somewhere between 60-70%. This means that 60-70% of the population will need to have immunity before the virus burns itself out and the population is resistant against future resurgence. Initial models that predicted 81% of the population were going to become infected with this virus were built around the assumption of homogeneity.

What happens when these models don’t assume that the exposure and susceptibility of each person is the same? What if some people are more susceptible to being infected and/or transmitting the infection to others? What if the population is modeled heterogeneously rather than homegenously? This seems like a much more reasonable approximation of reality than assuming every single person is the same.

But, does it make a difference to the HIT?

The answer is unequivocally YES. Big time.

Several papers from reputable epidemiologists who specialize in these types of mathematical models have recently made a very convincing, if not iron clad, argument that when incorporating population heterogeneity and fitting these models to COVID-19, that the HIT is somewhere between 10-20%!!!

At first glance, this might not make sense. How would differences among people cause the HIT to come down?

The real answer requires an understanding of the nuances of differential calculus, but a simple conceptual answer is this: If certain people in the population are more susceptible to becoming infected than others, these people become infected before less susceptible people and rapidly reduce the probability of other less susceptible people to becoming infected because these more susceptible people are rapidly progressed through the different buckets to the recovered pool (you may need to read that a few times slowly). This slows down the rate of infection and accelerates population based immunity.

To fit real data in one paper, the researchers had to employ probability distribution models that were bimodal to reach the low HIT levels being observed in other countries. What this means is that it is highly likely that a relatively small portion of the people are acting as super-spreaders (which implies vast heterogeneity).

Another factor that is more than likely causing an effective lowering of the apparent HIT is research showing that up to 80% of people have resident memory T -cells that can become activated when exposed to SARS-COV-2. These are people who have never been exposed to SARS-COV-2. This is presumably from previous exposure to the other four strains of coronavirus (that cause the common cold). If this proves out with further studies, a large portion of the population has some resident T-Cell mediated immunity to SARS-CoV-2 from prior exposure to one of the other coronavirus members. This is separate from the type of immunity imparted by antibodies, so seroprevalence studies that look for antibodies as a primary measure for immunity are more than likely underestimating the true state of immunity within a population.

Let’s be conservative and say that within the calculated range of 10-20%, that the HIT is 20% (to be conservative). This means that once 1 out of every 5 people have been infected, herd immunity has been achieved for this virus. Are we there yet in the US?

It’s important to remember that the virus knows nothing of manmade national boundaries, state lines, or county lines. It’s probably a gross over-simplification to apply the HIT level to the entire US due to the major differences in demographics.

Nonetheless, you can get an idea of the number of people who have been infected by the virus to date by looking at the number of people who have died, and back-calculating from the infection fatality rate. The infection fatality rate is somewhere between 0.2%- 0.3% (this is a population average, as this number greatly varies by age). The CDC puts this number at 0.26%. To account for 135,000 deaths to date in the US, this means that approximately 52 million people have been infected in the US, which is 16% of the population. This number may be somewhat of an over-inflation due to the different fatality rates based on age and the lack of actual infection data in calculating the infection fatality rate, but it demonstrates that a much greater portion of society has already been infected with this virus than the number derived from PCR tests. The actual number of measured cases in the US right now is about 3 million. Why the vast difference?

Well, it’s quite obvious that not every infected person has received a test. There’s not enough tests to go around to keep up with the infection rate, and most people are completely asymptomatic, so they don’t even think to ask for a test. That’s why looking at case rates by following the number of tests is completely arbitrary because it is limited by the number of administered tests.

So, it’s quite probable that we are well within the HIT range of 10-20%. Since we don’t know the exact number, we can only say that we’re probably close to being there. Remember, this is an average across the US, and if you zoom in regionally, you’re going to see regions that are much further away from reaching HIT, and regions that have already surpassed it. Because of the relative immobility and interaction of people across wide geographies, this could easily vary on a county by county basis. Also, the degree of heterogeneity in susceptibility and exposure on a local level based on demographics and policies will cause the HIT level to vary on a regional basis. For Stockholm, models showed HIT is 17%. But that is for that region, and that region only. NY city will differ from Lexington, KY, etc.

This is very good news. It doesn’t mean we’re not going to see increases in cases and deaths on a micro-regional level because each region has its own profile to play out, but on a macro-scale we are much closer to this being over than what was predicted in the models based on homogeneity.

Each state, city, and county should use these models to fit their data to calculate HIT, and how close they are to HIT. This will help to shape policy that protects people while minimizing the impact to the economy.

The best scenario for us is to reach the HIT without a vaccine. I believe we are close.

References are below if you’d like to read up on the math and models for yourself.

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References

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

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

https://www.researchsquare.com/article/rs-35331/v1

https://judithcurry.com/2020/05/10/why-herd-immunity-to-covid-19-is-reached-much-earlier-than-thought/

https://arxiv.org/abs/2005.03085

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