Maths matters

Author: Dr Wendy Burton, Australian GP, MBBS, FRACGP (Hon)

Expect the number of vaccinated people who are hospitalised, in ICU and dying from Covid-19 to rise even as the number of deaths per case falls. A small percentage of a large number can be a larger number than a large percentage of a small number

Life in Australia had been very sheltered from a COVID-19 infection perspective
But winter 2021 saw our case numbers increase as NSW and then Victoria battled with significant outbreaks, all the while racing to vaccinate their populations
What we saw as our case numbers exploded is the mathematical certainty whereby, with high vaccination rates, the majority of infections, hospitalisations, intensive care admissions and deaths occur in those who are vaccinated 

It's just a matter of mathematics

Let me explain

The maths is really very simple, until it’s not
Winter 2020, 100% of people admitted to hospital, ICU and dying of Covid-19 were unvaccinated as there were no vaccines
Imagine if we get to a stage where 100% of the population ARE vaccinated - at that point, 100% of people admitted to hospital, ICU and dying of Covid-19 would be vaccinated. The numbers would be less due to the power of the vaccines, but even so, 100% would be vaccinated because everyone is vaccinated

In Australia, we already have more than 96% of our over 16 year old population double vaccinated and 72.4% triple vaccinated

I'm now going to make some assumptions which are not actually true 

  • Let's assume that the death rate per number of COVID-19 cases is 1 per 100, i.e. 10 per thousand

    • It is actually higher than this, but this keeps the maths simple

  • Let's assume that the protection from infection due to COVID-19 following a double dose of vaccination is 50% 

    • It is actually much higher than this, but this keeps the maths simple

  • Let's assume that the protection from death due to COVID-19 following a double dose of vaccination is 90% 

    • It is actually higher than this, but this keeps the maths simple

Now let us assume that there are 1 000 people who have a COVID-19 infection who have been fully vaccinated and there are 1 000 people who have a COVID-19 infection who have not been vaccinated
Here are how the numbers would fall:

4.jpg

Now let us take another 2 000 people who have a COVID-19 infection and assume that 90% (1 800 people) are fully vaccinated and 10% (200 people) have not received their vaccines
Here are how the numbers would fall:

5.jpg

In fact, the maths is way more complicated than this
If we assume a situation where 100% of people exposed to the Covid virus would normally become infected (e.g. family quarantining with one person positive with the Delta strain), in order for 1 800 vaccinated people to become infected, more than twice that many would need to be exposed (once fully vaccinated, the risk of infection is less than 50%). For those who are not vaccinated at all, only 200 would need to be exposed
As we have witnessed during the pandemic, infectivity within the community varies dramatically, sometimes there is a “super-spreader” event, but mostly it is too hard to predict

So you can see that, the higher the percentage of vaccination within a community, the closer the absolute number of deaths from within the vaccinated community will be to the number from within the unvaccinated community. The same logic works when you look at how many become infected. Even though vaccination confers a significant amount of protection, the greater the number of people who are fully vaccinated, the closer the absolute number of vaccinated people who will be infected is to the number of unvaccinated people who will be infected

Number of deaths per 1 000 non vaccinated people with Covid-19.jpg

What you need to look at is not the absolute numbers but the percentages

Don't let people who do not understand or who are manipulating the maths trick you into believing that the vaccinations are not working

  • They do work

  • They are working

  • They are an essential part of the COVID-19 exit strategy for the entire world

Oct/Nov 2022 statistics from the CDC:

Rates of COVID-19 cases and deaths by vaccination status, Oct 2021 - Oct/Nov 2022

Unvaccinated: 171 cases and 1.17 deaths per 100k
Vaccinated: 68 cases and 0.19 deaths per 100k
Boosted: 57 cases and 0.04 deaths per 100k

Rates of COVID-19 cases and deaths by vaccination status, April 2022- March 2023:

Unvaccinated: 81.11 cases and 1.07 deaths per 100k
Vaccinated: 26.66 cases and 0.21 deaths per 100k
Boosted: 25.81 cases and 0.19 deaths per 100k

Disclaimer: This is not individual medical advice. Please follow your local, state or national guidelines and talk to your GP about your particular situation and healthcare needs