TORONTO -- The COVID-19 pandemic has introduced a slew of new phrases and concepts into the layperson’s lexicon, from “novel coronavirus” to physical distancing.

Data, too, has dominated coverage. Beyond the numbers associated with the daily total confirmed cases or deaths, one figure known as the “r-naught” (R0), or reproduction number, has been particularly common. The R0 measures the average number of secondary infections that any infected person may produce.

But as researchers learn more about the spread of SARS-CoV-2, the pathogen that causes COVID-19, another figure has been somewhat overshadowed in the process: the k number. It could be more representative of the pandemic and may inform more efficient forms of contact tracing.

“It’s basically a way of measuring if an infection, in this case a virus, will be transmitted in a pretty reliable manner or if it will be more spotty and often in clusters and in a less reliable manner,” infectious disease specialist Dr. Isaach Bogoch told over the phone. 

Early research shows that COVID-19 is not spreading in a “reliable” manner. Rather, it is often spreading in an “over-dispersed” manner, sometimes in what have been called “super-spreader” events, making an average figure like the R0 perhaps less representative of the reality of the pandemic. Since the spread is “spotty,” that means the k figure, measured on a scale of 0 to 1, is in the lower range. The SARS virus had a k value of about 0.16, while the flu pandemic of 1918 was around 1.0. Researchers estimate the the k value for COVID-19 could be around 0.1.


The figure helps inform decisions on how to prevent further spread and where to put the focus, said Dr. Andrew Morris, an infectious disease specialist with Sinai Health and University Health Network in Toronto.

He uses an analogy of a vehicle assembly line process. When there is a low level of dispersion, there may be a faulty car every so often and one in every 10,000 cars comes out irregular. But when there is a high level of dispersion, there is an identifiable issue among a “cluster.” On the assembly line, a problem might be identified, for example, during the 6 p.m. to 10 p.m. shift, said Dr. Morris. In his analogy, that shift is the overcrowded, unmasked nightclub, wedding or other social gathering.​


Researchers have been tracking the k number since the virus broke out late last year and new research continues to document it with more certainty. Earlier this week, a massive contact tracing study in India published in the journal Science found that as many as 70 per cent of infected people did not transmit the virus to anyone. But eight per cent of people accounted for 60 per cent, or three in five, new known infections. 

“Not everyone who has this infection is responsible for transmitting this infection equally,” said Bogoch. “There are some people and some conditions which really allow for much larger outbreaks than others.”

The wide spread of COVID-19 by small groups of people will rely on the confluence of a variety of factors, including the properties of the virus itself and the circumstances of an infected person’s environment.

“It’s probably like that Swiss cheese model where a few different things have to line up perfectly for this infection to really have a clustered outbreak,” said Bogoch. The first factor is of course the presence of an infected person. The others may include that person’s viral load. It’s probably that that person needs to be “shedding a lot of virus” to cause an outbreak, said Bogoch.

“Is it part of the upper respiratory tract where people can cough and shed more virus?” said Bogoch. “Or is it way down in the lower respiratory tract, where people might be less likely to shed as much virus?”

Environmental conditions may also play a role in why COVID-19 has a low k number. “You might have a lot of people in close proximity to that individual typically in an indoor environment for a prolonged period of time,” said Bogoch. “A wedding, a nightclub, a school where there are no protective measures in place.”


Many contact tracing models rely on a forward-thinking approach, meaning all the people that an infected person came in contact with after they were infected are informed. But some research suggests that, because of the low k number associated with COVID-19 dispersion, “backward contact tracing” may be a more apt model. An August paper published by the U.K. Centre for the Mathematical Modelling of Infectious Diseases found that “forward tracing” can typically identify just the “mean number of secondary infection,” or the R figure, while a retrospective approach taking the k number into account is likely to identify several more.

“In contrast, backward tracing increases this maximum number of traceable individuals by a factor of 2-3, as index cases are more likely to come from clusters than a case is to generate a cluster,” researchers wrote.

While Dr. Andrew Morris believes that more public health officials should be adopting the retrospective approach to contact tracing, the more important issue is prevention in the first place. 

“It’s far more important to get rid of the clustering by getting rid of scenarios where there is an opportunity for this to occur,” he said.