What is Herd Immunity?

Herd immunity, or community immunity, is when a large part of a population is immune to a specific pathogen or disease. A pathogen is an orgamism such as a virus or bacteria. Some pathegens will cause a disease. For example, SARS-CoV-2 is a virus that causes the COVID-19 disease. A person is immune to a pathogen or disease when they have a resistance to the pathogen.

Why is Herd Immunity Important?

When the resistance to a pathogen is good, the person does not have a welcoming home for the virus to thrive. The virus will die out in that person before it can be passed to another person. If sufficient people are resistant to the cause of a disease, such as a virus or bacteria, then, even if they catch the pathogen, then they do not have enough pathogens to spread to others and the virus is not spread to the community. Often the term "breaking the chain" is used to describe this situation. A vius spreads like a chain of connected persons. Person A passes the virus on to several other persons who, in turn pass it on. If a person receiving the vius does not pass it on, the chain of infection is broken. If enough chains of infection are broken then the vius dies out completely. Some perople in the herd may never encounter the virus as there are sufficeient people in the herd who are resistant to the virus and will not pass on those that have not been infected. So, while not every single individual may be immune, the group as a whole has protection. The infection rates drop, and the disease peters out.

Herd immunity protects the at-risk populations. Different pathogens have different at-risk persons. For the SARS-CoV-2 virus that causes the COVID-19 desease, these include the elderly and those whose immune systems are weak and can’t get resistance on their own.

How Much Herd Immunity is Required for COVID-19?

The amount of herd immunity required to protect the vulnerable in a population depends on a single factor. It is the transmission rate. This is the R values. There are several R values. One of the most quoted value is R₀ which is the trasnmission rate at the start of a pandemic or epidempic if no action is taken to prevent the virus passing between indiviauals. For the first wave of COVID-19 R₀ was believed to be around 3. That is, 1 person will infect 3 other people who will infect 9 people who will infect 27 people etc. However, some of the variants circulating at the start of 2021 are believed to have a R₀ value of 4. That is, 1 person will infect 4 other people who will infect 16 people who will infect 64 people etc.

The formula relating H to R for herd immunity to be effective is:
H > (1-1/R₀)
where H is the proportion of the population in the herd that has immunity. This is a value from 0 (no one has immunity) to 1 (everyone has immunity).

For a R₀ of 3, H equal 2/3 or 67%. For a R₀ of 4, H equal 3/4 or 75%.

How to Create Herd Immunity of 75%

One way is to for natural immunity to be aquired by being infected and recovering from COVID-19. This natural immunity is acheived by antibodies being created by the immune system to fight and nutralise the virus and desease. After the virus and desease have been defeated the antibodies stay around for some time and will fight and nutralise any new infection. For COVID-19 it is not clear how long the antibodies stay around. It could be as little as 4 months. It is not certain that natural immunity - which is short lived - would ever get the population immunity above 50%.

Another way to create immunity is by vacination. The current vacines appear to have a good efficacy. But, is it enough to get head immunity above 75%? We need an additional equation.
H = V * E
where:

H

proportion of the population in the herd that has immunity

V

proportion of the population that is vacinated

E

Efficay of the vacine where 1.00=100% and 0.75=75%

As an example, if 90% of the population is vacinated with a vacine that is 75% effective, then
H = 0.90 * 0.75 = .675
which means that there is 67.5% herd immunity. This is not good enough to cope with a virus that has a R₀ of 4. However, it is just enough to cope with a virus that has a R₀ of 3 as that only requires a head immunity of 67%.