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Herd Immunity - Why you probably won't get measles in Australia

Author: Gideon Meyerowitz-Katz

Date: 11/12/16

The other day I shared a fantastic infographic, and I was asked by a few people to elaborate. You may have heard about herd immunity (when I was in high school we actually had a science project dedicated to it), but there’s a good chance that you have never really had it explained.

It really is a great infographic; there is also a cool simulation at The Guardian, who made the thing

Herd immunity is a public health term that is one of the most important parts of the theory behind vaccination. It basically means the point at which there are enough people immune to infection to prevent people who are not immune from getting infected. It’s the reason that we don’t have to vaccinate every person to stop everyone from getting measles.

Pretty damn cool, I’d say.

A lot of herd immunity is about maths. I’ve handily italicized the maths for anyone who hates numbers. Skip away!

Attack rates, reproduction numbers and scary maths

As well as being one of my favourite public health terms, attack rate is a key part of herd immunity. It is a measure of the proportion of people who are infected by a disease in the population. Say there is a measles outbreak in a school of 100 kids. If 10 of those kids get measles, the attack rate is 10/100=10%. It’s a pretty simple metric to see how many people are infected in a population by a specific disease.

Along with the attack rate we can calculate a Reproduction Rate for the disease we are looking at, commonly called Ro. This reproduction rate is simply the number of individuals that are infected by each person who contracts the disease. The higher the number, the more people get infected. 

Measles has a very high reproduction rate, at 12–18 people infected, mumps is much lower at 4–7. On average, each person who has measles will infect about 3x as many new people as each person with mumps.

Herd Immunity

Most diseases are infectious for a week or so, although it varies greatly. Imagine you catch measles. You are infectious for a couple of days whilst only feeling minor symptoms (cough, runny nose). You then come down with a nasty fever, and after seeing the doctor stay at home for the rest of your infectious period.

In this example, you’ve limited your contact with uninfected people by staying at home once you realized you were sick. Even so, you’re still likely to have infected a significant number of people whilst you were wondering around, blissfully unaware.

But what if these people were vaccinated? If the vast majority of people you ran into on the street were already immune to catching measles, you might only pass on the disease to one person before going home. If they were all vaccinated, the outbreak of measles would stop with you.

This leads us to the Effective Reproduction Rate (called R). This is the rate at which a disease will spread given the percentage of a population that is already immune. It’s just the reproduction rate multiplied by the % of the population susceptible to the disease; if the Ro for measles is 18, and half of the population is immune, then R is 18x.5=9. In this population, each infected person will only pass on measles to 9 people, rather than 18.

This is how we calculate herd immunity. For a disease to be considered stable, each person can only on average infect 1 or fewer other people. In other words, R has to be less than or equal to 1.

For measles, Ro is 18. Therefore, 18x%=1, or 1/18=%. This means that the % of people who need to be vaccinated to prevent the spread of measles in a population has to be higher than 1–1/18, or ~95%.

This is how herd immunity works. It’s a simple mathematical function; if enough people are immune to a disease, it cannot spread beyond the initial infected person and dies out.

Why do people still get sick?

The first objection you’ll always hear when talking about herd immunity is “people aren’t cows”. This is stupid.

The second, less stupid objection is “people do still catch measles/mumps/German measles/love of the dance/typhoid/etc! That means herd immunity can’t work!”. Basically, if everyone’s vaccinated (and vaccines work), then how can anyone get sick?

Firstly, herd immunity is a simple mathematical function. The immunity can be conferred either through vaccination or just natural immunity; most diseases peter out without vaccination around the 90% infected mark, simply because enough people become immune.

The second reasons is simple; vaccination rates are often just not high enough to fully prevent diseases, particularly overseas. Some countries have had disease ‘eliminated’, which means that there is no reservoir of disease in the country, but many haven’t reached this point. Most of the disease outbreaks you see are people getting sick overseas and bringing it back to a vulnerable community who don’t have sufficiently high vaccination rates.

Why it matters

Herd immunity is important for one reason; not everyone can get vaccinated. For example, people who are undergoing chemotherapy for cancer have compromised immune systems and can get very sick if they receive certain vaccines.

But if enough people are vaccinated, they will be protected anyway.

Australia has some of the best vaccination rates in the world, with most areas topping 95% for the recommended vaccines. We have incredibly low rates of vaccine-preventable disease because of this.

But there are some communities who, for a number of reasons, have lower vaccination rates. Some of them have socio-economic issues with attending the doctor. Some think that vaccines are a secret government plot to make us into docile sheep*.

Whatever the reason, these communities lower the rates of protection, and end up putting us all at risk. Which is shit, because when people don’t get their vaccines, the most vulnerable are the first to suffer.

So protect the babies, old people and chemo patients and get your vaccines. You’re probably due for a booster right now.


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