How fractions can give a better understanding of what COVID-19 data shows about vaccinations

CBC has been hearing some common questions about COVID-19 numbers from listeners and readers. 

Callers and emailers have asked for help understanding why COVID-19 data released by the province seems to be showing one thing, when they're being told another.

The requests have often come in the form of two questions: 

1. Why are the numbers of vaccinated people contracting COVID-19 similar or comparable to the number of unvaccinated or partially vaccinated people getting COVID-19? 
2. If the numbers are similar, what is the point of getting the vaccine? 

These two questions are based around a misunderstanding. 

An expert that CBC News spoke with said it's not necessarily the individuals fault, rather it's a failure in how information is being presented to them. 

Take a look at this graphic shared by the Saskatchewan Health Authority. It shows the 131 new cases reported on Wednesday.

The graphic breaks down the 131 cases to show 103 were not vaccinated, 10 were partially vaccinated and 18 were fully vaccinated. 

The number of fully vaccinated people makes up a much smaller chunk of the cases reported on Wednesday, but it's not insignificant. 

Seeing the similarity in new case numbers for those who are vaccinated and those who are partially vaccinated can also give a misleading impression. 

Two experts said that just looking at the totals by themselves is the wrong way of thinking about this.

Andrew Cameron, a professor of biology at the University of Regina, and Nazeem Muhajarine, a professor of epidemiology at the University of Saskatchewan, both said it's better to think of those numbers as fractions.  

"We always need to look at look at a person as part of a group, as a part of a population," said Muhajarine.

That means treating the numbers shared on a daily basis as the numerator — the number above the line in a fraction — with the population of unvaccinated, partially vaccinated or fully vaccinated as the denominator — the number below the line in a fraction. 

There are hundreds of thousands more people vaccinated than unvaccinated in Saskatchewan. 

As of Wednesday, there were approximately 402,000 unvaccinated people (this includes kids under 12 who are not eligible), 93,000 partially vaccinated people who've only received their first dose and 678,000 fully vaccinated people. 

Lets put these numbers into fractions, using Wednesday's new case counts.

For unvaccinated people, there were 103 cases/402,000 people. For partially vaccinated, there were 10 cases/93,000 people. For fully vaccinated people, there were 18 cases/678,000 people.

We can then use these fractions to show a rate of how many people are being infected per capita in each group:

• Unvaccinated - 103 cases/402,000 people = approximately 26 cases per 100,000 people.
• Partially vaccinated -  10 cases/93,000 people = approximately 11 cases per 100,000 people.
• Fully vaccinated - 18 cases/678,000 people = approximately 3 cases per 100,000

Presenting these numbers as part of fractions like this can better illustrate why the figures aren't actually comparable, the experts said.

It can also help people understand why it's very important to get vaccinated. 

"What we're seeing is that the infections are concentrated in the unvaccinated individuals in the province," said Cameron. 

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Muhajarine and Cameron said it's good that the province is proactively releasing information that provides a better understanding of the state of COVID-19 in Saskatchewan. 

But Muhajarine also went a step further. He encouraged the province to provide a breakdown of the unvaccinated that shows the number of people who are contracting COVID-19 but are ineligible to get the vaccine.

"That is more transparent, more helpful and more able to communicate the importance of getting a vaccine for those who are eligible and not getting the vaccine," Muhajarine said. 

Currently anyone under the age of 12 is not able to receive a dose.

Approximately 155,000 people fall into that category, according to the province's population estimates. 

Cameron and Muhajarine both emphasized that vaccines don't provide immunity to COVID-19, but they do provide significant protection against contracting the virus, curbing the worst symptoms of COVID and limiting the spread. 

"[A vaccinated person is a] very hard barrier for that virus to pass through because it's harder for the virus to infect in the first place and then it's harder for the virus to jump to the next person," said Cameron.