I'm an internist, trained in epidemiology and public health at Johns Hopkins, and

the founder of Medmastery, where we teach important clinical skills to doctors and

other healthcare providers around the world.

Today we're going to talk about herd immunity and how to stop an epidemic.

Let's get started.

So what is herd immunity?

Well, it's a basic principle that's used in combating epidemics.

Herd immunity occurs when a significant proportion of the population or the herd

have been vaccinated or are immune by some other mechanism, resulting in protection

for susceptible individuals.

Let's see how this works in action.

In a previous video we talked about R naught, the basic reproductive ratio.

Let's look at this example where we have one diseased or infected individual and 18

susceptible individuals.

As you might remember, R naught is the average number of individuals an infected

person gives the disease to.

R naught is fairly constant for a given disease.

R naught for the novel coronavirus SARS-Co-2 has been estimated to range

somewhere between two and three.

So let's say this COVID-19 patient gives the disease to these three individuals.

And let's say these three individuals give the disease to three other individuals in

turn.

Then this is what the situation will look like after some time.

Now, let's assume that we vaccinated some of these susceptible populations, such

that they became immune to the virus.

Now the virus can't infect individuals it infected in the previous scenario.

Now our index case only infects one other person, and due to the immunity or herd

immunity of the group, this newly infected case can also only infect one other

person.

What we've done here is to reduce the basic reproductive ratio of three to an

effective reproductive ratio of one.

As we've seen in a previous video, when R is equal to one, the disease remains

stable and won't grow.

The herd immunity threshold is the proportion of a population that needs to

be immune in order for an infectious disease to become stable in that

community.

Or in other words, in order for R to become equal to or lower than one.

If this is reached, for example, through immunization, then each case leads to a

single new case and the infection will become stable within that population.

So how do we know what proportion of the population needs to be immunized in order

to reach herd immunity?

Let's look at a disease with an R naught of eight, or one infected individual

infects eight others on average.

What would need to happen for them to only be able to infect one other person?

Well, we would need to immunize these seven over here.

So seven divided by eight or seven eighths is the herd immunity.

It's calculated as R naught minus one divided by R naught.

As we've learned previously R naught for SARS-KoV-2 is between two and three.

So how many people would we have to vaccinate, if there was a vaccine in order

for the epidemic to stop?

Well, that's two minus one divided by two, which is one half or 50% if R naught was

assumed to be equal to two.

And three minus one divided by three or two thirds if R naught was assumed to be

equal to three.

So according to this calculation, we'd have to vaccinate between 50 and 66% of

the population.

Now, I recently heard Marc Lipsitch an epidemiologist from Harvard mention in a

podcast interview that the herd immunity of COVID-19 according to his data, was

around 40%.

I'm sure he has more complex tools to factor in other variables that could

influence herd immunity.

But if you want to go by the books, the calculation of herd immunity according to

the formula we provided is valuable and valid.

By the way, I really recommend you follow Marc on Twitter.

He provides great insights about the epidemic and seems to be a super smart

guy.

That's it for now.

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