Topic 10.3
What is the immunity threshold, and how does it help control the spread of infectious diseases?
How do we stop diseases from spreading? We can reduce the reproduction number below 1 by achieving an immunity threshold, stopping outbreaks. This page will explore immunity thresholds and the different thresholds for different diseases.
Immunity Threshold
If, on average, one sick person causes 10 others to get sick, then the basic reproduction number is 10. Those 10 people will each cause 10 others to fall ill, so 10×10 means 100 more people become ill, and now we have an epidemic.
This slows down quite a bit if lots of people are immune.
Some very cool and simple statistics use the reproduction number to determine how many people need to be immune to a particular infection, like measles, to prevent it from spreading. This is called the Immunity Threshold.
You can be immune because of vaccination or by having recovered from a bout of measles. What proportion needs to be immune to stop a particular infection from spreading?
The aim is to reach the stage where the reproduction number is under 1. That means that not every case causes another case, and the chain of infections eventually stops
Immunisation is the safest way to achieve this.
An Example
Let’s say a case of measles is caught overseas and brought back on a plane by an ill child to Australia.
If the reproduction number of that germ is 10, there could soon be an epidemic.
We need to get the reproduction number down to less than one, where not every case causes another case, and the chain of infection stops, causing the disease to burn out.
How?
Well, if 90% (9 in 10) of the population are vaccinated against measles and immune, only 1 person in 10, on average, can catch measles from the imported case.
This is called the “immunity threshold” – scientists use the immunity threshold to determine if herd immunity can be achieved.
There’s a simple mathematical equation to find out what the immunity threshold:
1 minus ( 1 divided by ‘reproduction number’)
= 1 minus (1 /10)
= 1 minus 0.1
= 0.9
Otherwise known as 90%
So, having at least 90% immune can prevent an infection from spreading!
Why not work out the immunity threshold for a different virus?
What percentage (threshold) of people need to be immune to stop its spread when a virus has a Reproduction number of 2?
Click to reveal the answer!
Answer: 1 minus 1/2 = 0.5 (50%)
Different thresholds for different diseases
Some vaccines work better than others. For example, Measles and the Omicron (COVID-19) spread easily – each with a basic reproduction number of about 10. The measles vaccine is very good at eliminating measles in a community. Almost no one gets sick if they have been vaccinated.
The COVID-19 vaccine makes people less likely to get sick. About 50% of people can still get a very mild infection (called a breakthrough infection). The COVID-19 vaccine stops about 90% of people from becoming sick or dying.
So, many experts consider herd immunity to COVID-19 to be a real challenge. COVID-19 vaccines do not achieve “sterilising immunity”. There are people, like babies, the elderly and cancer sufferers, who can’t be vaccinated. They rely on everyone else getting vaccinated for protection.
The first version of SARS (a related coronavirus) was discovered about 20 years ago (SARS-CoV-1), and vaccine research has been ongoing for years. COVID-19 is caused by SARS-CoV-2. The vaccine developed in 2020 was based on decades of research. It was not done quickly.
Without vaccination, COVID-19 would have caused far more damage to society. Millions of lives have been saved by COVID-19 vaccination. Vaccinated people are less likely to transmit infection. This saved people who could not be vaccinated. The AstraZeneca vaccine has been used in 175 countries and billions of people. The Pfizer vaccine and Chinese vaccines are the next most commonly used.
The Black Death killed 25 million people over 4 years in Europe during the 1300s. That’s similar to the entire population of Australia. There was no vaccine, only public health measures like quarantine.
Vaccination saves lives and creates the safest path to possible herd immunity.