It's been 2 years since I posted this blog, and it's still one of my favourites.

Here's a tweetorial on herd immunity, and why it's pretty cool #VaccinesWork medium.com/@gidmk/herd-im…
First, let's get something out of the way:

Herd immunity has nothing to do with cows! Saying "people aren't cows" is just displaying your ignorance for all to see
So, what is herd immunity?

At its most basic level, it is simply maths
A more useful definition, however, is that herd immunity is the point at which enough people are immune to a disease to prevent non-immune people from getting it
The first part of herd immunity is the attack rate (AR) of a disease. This is fairly simple - it's the rate of infection due to a disease in the population

Mathematically, this means x/n = AR where x is the number of infected people and n is the total population
If you have a school of 100 children, and 10 of them get measles, the attack rate would be
The answer is fairly easy here - 10 children, total n of 100, so AR = x/n = 10/100 = 0.1 = 10%

As I said, a simple metric of how infectious a disease is in practice
The next important number is the reproduction rate (R). This is similar to the AR, but it looks at the number of people who get the disease from each infected person

The higher the number, the more infectious the disease
(Sorry, small correction. The reproduction rate is usually abbreviated to R0, not R. R is the abbreviation for the EFFECTIVE reproduction rate, which we'll get to)
Here are some common R0s for various vaccine-preventable diseases, as per the CDC

You can see why measles is such a problem!
So this is the reproduction rate of the disease in an entirely vulnerable population. It's pretty simple - you look at each person, check their contacts - people they interacted with while infectious - and see how many get the disease

What happens if people are immune?
Here's where the maths comes in. Now, immunity can be conferred by vaccines, but it doesn't HAVE to be. Even without vaccines you start seeing herd immunity once 90%+ of the population has been infected
(The downside to this, of course, is that most people get sick and some die from the disease to earn that immunity, whereas vaccines are much safer)
More
The EFFECTIVE reproduction rate (R) is calculated based on the R0

Mathematically, it is: R0*y = R

Where y is the proportion of the population susceptible to the disease
Based on the table above, what's the R for measles in a population with 75% vaccination rates?
Here's a more difficult question - based on the equation for R, what is the formula to work out the % for herd immunity (HI)?
This is more complex because you have to think about what herd immunity really means

Herd immunity means that each person passes on the disease to fewer than 1 person (on average), so the disease eventually peters out
What this means, in technical terms, is that R<1

I.e. the effective reproduction rate in the population is less than 1
Mathematically, this gives us the minimum threshold for herd immunity as:

R0*(1-HI) = 1

Where R = 1 and R0 is calculated based on the disease

Turning this around, we get:

HI =1-(1/RO)
So to work out the threshold for herd immunity, we just have to solve this for each disease!

Pretty cool, huh?
What's the herd immunity threshold for mumps, based on this formula?
Completing the formula, we get:

HI = 1-(1/4) to 1-(1/7) = .75-.86 = 75-86%
What this means is that we have to vaccinate 75-86% of the population to reach the threshold for herd immunity for mumps
The more infectious the disease, the more you have to vaccinate

Measles can live for hours, even days, outside the body, and has an R0 of >12, which means that we need to vaccinate 95% of the population to be sure it won't spread
Smallpox only has an R0 of 7, which means that we only had to vaccinate ~85% of people to eliminate the disease
And that's it. That's how herd immunity works

Simple, easy, incredibly, wonderfully powerful
People do still get these diseases. No vaccine is 100% effective - although many are close to that - so vaccination rates often have to be higher than even the theoretical herd immunity threshold
There are also a lot of people who have been scared away from vaccination by anti-vaccine activists who spread fear about lifesaving medical interventions #VaccinesWork
But we know that vaccinations WORK

Australia has now eliminated endemic measles and rubella, and almost entirely eliminated many other infectious diseases, with some of the highest vaccination rates in the world #VaccinesWork

They will not only stop YOU from getting sick, they'll also stop you from passing diseases onto more vulnerable people like babies and immunocompromised people #VaccinesWork
And the next time someone says "herd immunity is a myth!", feel free to reference this thread and/or blog

Herd immunity is simple maths, nothing more, nothing less
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