COVID-19 modelling explained: The calculations used to make public health decisions in Sask.

The first phase of Saskatchewan reopening plan started Monday, but the province has said repeatedly that it will be closely monitoring case numbers to see if it needs to reinstate tighter restrictions. 

Last week the Saskatchewan Health Authority (SHA) detailed one of the calculations it is using to determine whether or not the curve is staying flat in Saskatchewan: the effective reproductive number, or Rt.  It said the Rt would be used to signal when numbers in the province are rising and when changes to the reopening plan might be needed. 

Previously, the health authority had only shared modelling based on a different calculation — the basic reproductive number, or R0 (pronounced R-naught) — based on how the virus behaved in different parts of the world. It said at the time there was not enough Saskatchewan data to develop models based on local numbers. 

Rt, which the province said will be released weekly, provides more current information about the rate of transmission in Saskatchewan.

With decisions about what should be reopened — and when — relying on these numbers, CBC asked an expert in the field to further explain these calculations and how to interpret them.

Dr. Cory Neudorf is a University of Saskatchewan professor in the department of community health and epidemiology.

He gave insight into both the Rt calculation and how the R0 has been used to establish the worst-case scenarios released by the province. The R0 is still being used to prepare for a potential surge in cases.

The basic reproductive number 

The basic reproductive number, or R0, is designed to describe how infectious one disease is compared to another.

It is based on what the virus would do without interventions such as travel restrictions, social distancing and increased hand-washing. 

"It's really just describing on an average level how many people are likely to get infected from one other previous case," said Dr. Neudorf. 

The SHA uses the R0 number to establish a worst-case scenario for COVID-19 in Saskatchewan and, in turn, to make plans accordingly. 

The most recent modelling from the province outlined a worst-case scenario of 3,000 deaths from an overall 255,000 cases. This was based on an R0 of 3.12. 

SHA representatives were asked last week to explain why the province is basing its planning on "worst-case" numbers, which appear much higher than what the province is experiencing now.

They said at a news conference that R0 modelling is needed to help the system prepare for a surge in cases if that happens.

The officials said it is not a projection of what will happen, but a plan to ramp up a big, complex health system that cannot turn on a dime.

"We all really hope that we don't see anything like this but we need the system to be able to prepare, to be prepared to actually respond should this happen," said Derek Miller, the SHA Emergency Operations Centre Lead.

"When we see situations like you might see in New York or other jurisdictions where things flared up really quickly, we want to make sure that our system is also able to really stand up really quickly to respond to that." 

Effective reproductive number

Rt, the effective reproductive number, reflects the current rate of transmission based on what is happening in the province right now. 

An Rt of one would mean each person to get the virus would be expected to infect one other person on average.   

On April 28, the day the number was released, the province said Saskatchewan had an Rt of 0.7. 

"Basically all of these numbers are calculated on an average. So if you think about it let's say you take a hypothetical 10 people who have COVID-19. If the reproductive number is 0.7, those 10 people would [collectively] infect seven new cases," said Neudorf. 

"So those 10 people recover or are hospitalized or in some cases die. But there's seven new cases to contend with. If that reproductive number continues to be 0.7 there's again fewer cases, probably five that result from that group." 

The SHA described Rt as a "guidepost" for choosing when to implement new measures or loosen existing ones. 

"What the model will help us do on a daily basis, weekly basis, monthly basis, is allow us to measure what's happening in the province, whether it's us reopening the health care system or the economy continuing on in phases," said Scott Livingstone after the release of the Rt last week. 

Modelling from the province said the tipping point is an Rt of 1 — that's when the number of cases begins to grow. 

"A reproductive number of 1 means every new case produces another new case so the 10 people would infect 10 more, so things stay at the same level depending on whether people get infected quicker than people recover, though, you can see cases expand slightly," Neudorf said.

"Then if the number is higher than one obviously that's when you see outbreaks grow because then every person, let's say that the reproductive number was two, every 10 people would be having 20 new cases."

Neudorf said the difference between an Rt of 0.7 to an Rt of 1 is significant. 

Asked at what point tighter restrictions would need to be reinstated to avoid a number of 1 or higher, he said it would be important to consider how much time has passed between the Rt number increasing from, for example, 0.7 to 0.8. 

He said the number is always a week or two behind the actual rate of transmission because it is picking up cases that became infected days earlier — and only then doing contact tracing.

"Anytime you have a movement, if it's moving closer toward one, you have to think forward. What is it like right now based on the number I am looking at? Is it really last week's number or or even the week before that?" said Neudorf. 

Saskatchewan's Rt number is currently calculated based on numbers from the whole province. 

SHA senior medical information officer Dr. Jenny Basran said last week there are efforts underway to develop Rt numbers for each region individually, but no specific numbers for outbreak areas, such as La Loche or Lloydminster, have been released at this time.

Neudorf said the rate of transmission will be dependent on the level of adherence with public health advice. 

He said continued social distancing is key to keeping the Rt low. 

Neudorf said members of the public should keep that in mind as the provincial re-opening plan begins. 

"There's some anecdotal reports [that] all that people heard [from the reopening announcement] was 'reopened,'" he said. 

"So I think it's very important for people to see this is just one indicator to show of we are being successful or not. 

"We're going to have to just remember that it's not back to normal, it's back to a new normal that includes some of those restrictions for the foreseeable future."