When deciding how and when lockdown restrictions will be lifted across the UK, the government has said the R value, denoting how many people on average one infected person will themselves infect, is crucial. But experts say another metric is becoming increasingly important: K.

What is K?

K sheds light on the variation behind R. “Some [infectious] people might generate a lot of secondary cases because of the event they attend, for example, and other people may not generate many secondary cases at all,” said Dr Adam Kucharski, an expert in the dynamics of infectious diseases at the London School of Hygiene and Tropical Medicine.

“K is the statistical value that tells us how much variation there is in that distribution.”

But unlike R, K numbers are not intuitive. “The general rule is that the smaller the K value is, the more transmission comes from a smaller number of infectious people,” said Kucharski.

“Once K is above about five or 10 it tells you most people are generating pretty similar numbers [of secondary cases], you are not getting these super-spreading events. Once K is below one, you have got the potential for super-spreading.”

Is K fixed, or does it fluctuate with public health measures, like R does?

As with the rate of transmission, there is a K value that relates to transmission when you do not have any control measures in place. Once measures are implemented, however, the distribution in transmission changes. “It is unlikely that with lockdown measures in place you’d see a lot of super-spreading events simply because there aren’t any opportunities for them,” said Kucharski. “So if you were to analyse that data, you’d probably calculate a different K value because you have got those control measures changing the dynamics of interactions.”

What is the K number for Covid-19?

In the absence of public health measures, “the values that are coming out for Covid-19 seems to be between about 0.1 and 0.5,” said Kucharski. That, he says, means that in the early stages of an outbreak about 10-20% of infections probably generate about 80% of the transmission.

In other words, super-spreading matters – a reality highlighted by reports such as that from South Korea where one individual is thought to have infected dozens of others by attending church.

But Kucharski cautioned against the use of the term super-spreader. “I think we do have to be really careful about blaming people because often it is not really much about the person, it is much more about the environment they happened to be in while they were infectious,” he said.

Why is K important?

Knowing the K value helps to inform what sort of public health measures may help to reduce R.

“If we can identify and reduce the situations that are disproportionately driving transmission, then that suggests that we could actually have potentially quite a lot less disruptive measures in place, but still keep the reproduction number low,” said Kucharski.

But it could also be important for test-and-trace measures, he said. “If cases occur at random, it’s very hard to track down and stop every chain of transmission. But if cases cluster together, and we can identify those clusters, testing and tracing directed at these situations could have a disproportionate effect on reducing transmission.”

How might the relaxation of the lockdown affect K?

Lockdown reduces the chances of a single infectious person spreading the disease to others. “Obviously if you start to allow larger gatherings, have larger workplaces, if you have other types of interaction starting, then that does increase the chance that one infection could spread to more people than it would have been able to a couple of weeks ago,” said Kucharski. “It could decrease the K, but it could also increase the R.”

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