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# What Is Herd Immunity Threshold? Herd Immunity in Humans, Vaccinations, and Covid-19

Ryan Johnson, Terry Dunn
• Author
Ryan Johnson

Ryan has tutored high school and college level math and science for over a decade, and has taught in a classroom setting for more than two. He has a BA in Chemistry from Ferris State University, and an MA in Archaeology from the University of Kansas.

• Instructor
Terry Dunn

Terry has a master's degree in environmental communications and has taught in a variety of settings.

What is the Herd Immunity Threshold? How does herd immunity function? Learn the heard immunity definition and how different viruses and different thresholds occur. Updated: 08/23/2021

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## What Is Herd Immunity Threshold?

When an infectious virus is introduced into a population, there will be people who are immune to it and people who are susceptible to it. As the proportion of immune people in the population increases, the chance that the virus will infect a susceptible person decreases. The Herd Immunity Threshold (HIT) happens when that chance gets close to zero, so that a susceptible person is very unlikely to be infected because of mass immunity in the group. The "herd," of course, is the group of people. Herd Immunity is also called Population Immunity or Community Immunity. Discussion about HIT has been particularly relevant in 2020 and 2021 as we look for ways to bring an end to the Covid-19 viral pandemic. Can herd immunity work for us? What does it take to reach the threshold? Has it ever been done before?

## What is Herd Immunity?

Do you ever consider yourself part of a herd? I don't know about you, but when I think of a herd, I think of cows and wildebeest, not people. However, in terms of herd immunity, humans may as well be part of a flock, a gaggle, or a pod. We are part of a larger group and our individual immunity is entangled in the immunity of the people around us.

Immunity is an organism's ability to fight off infection. This happens when antibodies or special white blood cells spring into action to defend the body from infection. Herd immunity is more complex and has to do with protecting the whole population from a disease by immunizing a threshold number of individuals. After a certain level of immunization is reached, there are not enough people with the infection to spread it to other people. Once that threshold is reached, the disease stops infecting new people.

## Herd Immunity: Definition and History

The study of herd immunity begins in the 20th Century. While William Farr had written about smallpox-vaccinated individuals slowing outbreaks of the disease in 1840, it was concerns about livestock that essentially founded the idea and gave us the term. American farmers in the 1910s were battling the spread of a lethal condition that affected pregnant cows. In 1918, Kansas veterinarian George Potter realized that the way to fight the disease might be to let affected cows recover. The herd would then eventually become entirely comprised of immune cows. Potter wrote, "Herd immunity is developed, therefore, by retaining the immune cows, raising the calves, and avoiding the introduction of foreign cattle."

Over the next decade, discussion about herd immunity in humans arose, especially after the twin scourges of the 1918 Influenza Pandemic and World War I, in which millions of soldiers and civilians died from diseases such as the flu and typhoid. The term was first published in a 1923 paper by William Whiteman Carlton Topley and Graham Selby Wilson. Topley, a bacteriologist, had experimented on groups of mice, infecting them and observing that the disease would die out unless new, susceptible mice were continuously introduced to the group. Local herd immunity was observed in groups of children during measles outbreaks in the 1930s.

In the midst of the Covid-19 pandemic, talk of herd immunity, and especially the HIT, has been front and center, with some officials openly mentioning it as a possible strategy.

## How Does Herd Immunity Function?

Herd immunity works by limiting the options of an infectious disease. When there are a lot of susceptible people in a group, the virus has many avenues to spread. If an infected person coughs or touches a door handle, there will likely be another susceptible person along to carry on the infection. If there are immune people in the group, then the virus has a problem, and if there are a lot of immune people, the virus has a big problem. If there are enough immune people, the Herd Immunity Threshold is reached and the tables are turned. The virus can no longer spread, and it will die out.

This basic description of herd immunity, then, requires three assumptions:

1. An individual can only be infected one time
2. An immune person can't be a carrier
3. The population is evenly mixed

We can show how this works with with pen and paper.

### Reaching Herd Immunity

The herd immunity threshold can be reached in three ways: vaccination, natural immunity, or a combination of both.

Vaccination has the advantage of giving direct immunity without ever having been infected, and we can track the percent of a population that has been vaccinated. A vaccine is a human-created defense against disease. In a lab, dead or inactive viruses are used to create a compound that, when injected, will cause an organism's immune system to react as if it has been infected. It hasn't been infected, but it will produce antibodies, special molecules that defend the body against a particular virus. That way, when the live virus is encountered, the immune system is ready for it, and will fight off the virus before infection can occur.

Natural immunity includes those who are innately immune to a particular virus due to their genes, but also people who have already been infected. Once a person recovers from a particular virus, they are often immune from reinfection, at least for some time. As more and more people get re-infected, the number of naturally immune people increases.

In reality, it is usually the combination of the two that works towards herd immunity. As more people are vaccinated and more people are infected, the number of immune individuals grows and the population gets closer to reaching the Herd Immunity Threshold.

### Virus Reproduction Number

The value {eq}R_0 {/eq}, R(0), or R naught is defined as the average number of people that will be infected by a contagious person if everyone in a population is susceptible. If R(0) = 3.0, an average host will infect 3 more people. In general, a disease with where R(0) > 1 will spread, and one where R(0) < 1, will die out on its own. It should be noted that R(0) is for a completely susceptible population, and it does not change. The value R applies to a population with immune members. It can change as vaccination and infection numbers change, and R < 1 can mean that an epidemic will end.

The Herd Immunity Threshold is related to R(0), in that the HIT is essentially the inverse. It can be calculated using:

$$HIT = 1- \frac{1}{R_0}$$

Therefore, a virus where R(0) = 2.0 has an HIT of 50%.

## Herd Immunity Threshold

Different viruses will have different R(0) values and Herd Immunity Thresholds. Reaching that threshold or otherwise controlling the spread of different viruses can be complicated and requires different strategies. Some viruses with high R(0) values are basically unavoidable until vaccination becomes common. Some, like the flu, still manage to avoid being pinned down by yearly vaccinations.

Disease name R(0)
Measles 12-18
Chicken Pox 10
Polio 5-7
Influenza 0.9 - 2.1
Ebola 2
1918 Flu 1.4-2.8

Covid-19 has an R(0) of around 4, so it has an HIT of 75%. As of August 2021, around 50% of the US population has been vaccinated.

### Measles

In the US, measles is a childhood disease that used to be serious health matter. Having an R(0) value of 18, it is highly contagious, and it has an HIT of around 95%. It is now controlled with scheduled vaccinations, and the US has effectively reached herd immunity (with the occasional small outbreak). Worldwide, however, measles kills 100,000 children each year, and vaccination efforts are hampered by the fact that so many children catch it very early in life. Their temporary, natural immunity after recovering interferes with the vaccine's effectiveness, and it can be hard to administer an effective vaccine later in life before they get infected again.

## The Nuances of Herd Immunity

Maybe that doesn't seem too complicated on the surface, but immunity and human behavior is not so simple. Some diseases are easier to transmit than others. Some vaccines aren't 100% effective. Some populations are hit harder by certain diseases. And not everyone makes decisions the same way.

So, in terms of the threshold needed for herd immunity against a particular disease, it depends on how many people have a chance of being infected by one sick person. For instance, one person with measles is likely to pass it to 12 to 18 other people. One person with polio is likely to transmit it to 5 to 7 other people. Both of those diseases have vaccinations available to prevent them. But, if only a few people are vaccinated and someone gets sick, a lot of other people are probably going to get sick as well. However, if most people are vaccinated or have immunity, then one sick person simply can't make many other people sick. The threshold of the group's immunity for measles is 95%. That means 95% of the population needs to have immunity to keep measles from spreading. For polio, the threshold is 80 to 85%. If a vaccine is less effective, then the threshold might need to be higher because some people who got the vaccine might not be fully protected. They can catch the disease and even a mild case can still infect others.

People are not always the same when it comes to vaccinations and immunity. Infants, for example, don't have a lot of natural immunity when they are born, but they also can't get vaccinations right away. So, they depend on herd immunity to protect them. If a disease isn't affecting people in the population, it can't be transmitted. But sometimes focusing on the immunity of only certain groups within a population protects other groups. For instance, targeting school kids for flu vaccines ends up protecting elderly people, who have a harder time fighting off the flu.

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## What is Herd Immunity?

Do you ever consider yourself part of a herd? I don't know about you, but when I think of a herd, I think of cows and wildebeest, not people. However, in terms of herd immunity, humans may as well be part of a flock, a gaggle, or a pod. We are part of a larger group and our individual immunity is entangled in the immunity of the people around us.

Immunity is an organism's ability to fight off infection. This happens when antibodies or special white blood cells spring into action to defend the body from infection. Herd immunity is more complex and has to do with protecting the whole population from a disease by immunizing a threshold number of individuals. After a certain level of immunization is reached, there are not enough people with the infection to spread it to other people. Once that threshold is reached, the disease stops infecting new people.

## The Nuances of Herd Immunity

Maybe that doesn't seem too complicated on the surface, but immunity and human behavior is not so simple. Some diseases are easier to transmit than others. Some vaccines aren't 100% effective. Some populations are hit harder by certain diseases. And not everyone makes decisions the same way.

So, in terms of the threshold needed for herd immunity against a particular disease, it depends on how many people have a chance of being infected by one sick person. For instance, one person with measles is likely to pass it to 12 to 18 other people. One person with polio is likely to transmit it to 5 to 7 other people. Both of those diseases have vaccinations available to prevent them. But, if only a few people are vaccinated and someone gets sick, a lot of other people are probably going to get sick as well. However, if most people are vaccinated or have immunity, then one sick person simply can't make many other people sick. The threshold of the group's immunity for measles is 95%. That means 95% of the population needs to have immunity to keep measles from spreading. For polio, the threshold is 80 to 85%. If a vaccine is less effective, then the threshold might need to be higher because some people who got the vaccine might not be fully protected. They can catch the disease and even a mild case can still infect others.

People are not always the same when it comes to vaccinations and immunity. Infants, for example, don't have a lot of natural immunity when they are born, but they also can't get vaccinations right away. So, they depend on herd immunity to protect them. If a disease isn't affecting people in the population, it can't be transmitted. But sometimes focusing on the immunity of only certain groups within a population protects other groups. For instance, targeting school kids for flu vaccines ends up protecting elderly people, who have a harder time fighting off the flu.

To unlock this lesson you must be a Study.com Member.

#### What percentage of the population must be vaccinated to achieve herd immunity for COVID-19?

The Herd Immunity Threshold is the percent of a population that needs to be immune for herd immunity to happen. It is calculated with the equation

HIT = 1 - 1/R(0)

R(0) is the virus reproduction number. For a virus, it is the average number of people that a person carrying the virus will infect. An R(0) of 5 means that an infected person will on average infect 5 more people.

Covid-19 seems to have an R(0) of around 4. If that is the case, then the HIT is 75% immunity.

#### Can I still get Covid after the vaccine?

Infection can occur in vaccinated people. The vaccines available today provide very strong protection, about 95%, so there is still a small chance that a vaccinated person will get Covid-19. However, the vaccine also has the added benefit of preventing more severe symptoms if infection does happen.

On top of that, vaccination helps everyone. If more and more people are carrying around the 95% protection, it limits the spread of the virus in general.

#### How is herd immunity achieved for COVID-19?

Herd immunity is achieved for Covid-19 (or any disease) by reaching the Herd Immunity Threshold (HIT). The HIT is the percent of a population that needs to be immune so that herd immunity can take place. For a virus it can be calculated with

HIT = 1 - 1/R(0)

Where R(0) is the virus reproduction number. R(0) is the average number of people that a person carrying the virus will infect. An R(0) of 5 means that an infected person will on average infect 5 more people.

Covid-19 seems to have an R(0) of around 4. If that is the case, then the HIT is 75% immunity, either through vaccination or immunity through previous infection.

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