A short thread on herd immunity.

Herd immunity is an incredibly important concept. It suggests diseases can be eliminated without everyone having immunity.

If you want to eliminate an established disease then herd immunity is the way to do it.

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It's important to note that people can gain immunity in two different ways. Through being infected and recovering with immunity or through being vaccinated.

Hard to believe it needs to be said but, the best way for people to get immunity is through vaccination.

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When enough people have immunity for the reproduction number to go below one the disease will start to decline.

This level of immunity is often called the herd immunity threshold or the critical immunisation threshold.

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For very simplistic mathematical models the proportion of people who need to be immune is given by 1-1/R0, where R0 is the basic reproduction number (i.e. the number of people each new infectious individual will pass the disease on to in an entirely susceptible population)

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This is because the current reproduction number is
R=R0*(1-p), where p is the proportion of the population that is immune (and (1-p), therefore, the proportion not immune).
If p=1-1/R0 then R=1, the tipping point at which infection should start to decline.

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This is a very simplistic picture but is useful for back of the envelope calculations.
In reality many factors will influence the herd immunity threshold.
They include:

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a. Heterogeneity of the population - i.e. taking into account the fact that not everyone mixes with everyone else equally.
This is particularly important when we are vaccinating by age brackets who will not mix equally with each other. Immunity will not be spread evenly.

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b. The degree of immunity - vaccines, for example, do not provide 100% immunity. This means the herd immunity threshold will be higher.
The potential for immunity to wane also means we will need to up the numbers of people vaccinated.

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Even if we reach a theoretical herd immunity threshold through vaccination, if there are large demographics that are not immune then the disease can still spread freely in these groups.
So, in many senses, talking about "the herd immunity threshold" is not helpful.

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Herd immunity means a disease can die out without us having to vaccinate everyone. We can protect people who can not get the vaccine for one reason or another.
We do, however, need to remember that there are caveats when talking about herd immunity thresholds.

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