*Until Covid-19 struck the world, most of us had never encountered R. Now, many of us are speaking about R as though we really understand why it must drop below one. Some of us have been getting hot-under-the-collar about whether herd immunity should be encouraged. But how much do we really know about these statistical concepts that have entered the mainstream lexicon as governments try to explain why entire nations must remain under the equivalent of house arrest in order to re-shape a curve that tracks the spread of the deadly coronavirus? The Wall Street Journal demystifies these all-important concepts and introduces us to Ro, so the next time we engage in Covid-19 debate, we are better equipped to assess the danger. – Jackie Cameron*

___STEADY_PAYWALL___

## The numerical language of Covid-19: A primer

The figures are related, but differ in meaning and magnitude.

R0 isn’t the same as R. Herd immunity differs from final epidemic size. And not all death rates are created equal.

Understanding the difference helps policy makers appreciate how to calculate risk and allocate resources as a pandemic unfolds. Mixing them up distorts reality.

R0 (pronounced “R naught”) is a pathogen’s basic reproduction number and represents the number of new infections caused, on average, by a single contagious person. It anticipates a worst-case scenario that assumes the entire population is susceptible, well-mixed and taking no precautions to mitigate the spread of the disease.

The R0 of the new coronavirus, according to estimates by epidemiologists at Imperial College London, is 1.5 to 3.5.

If a pathogen’s basic reproduction number is less than one, a pandemic won’t take off. If the number is greater than one, an outbreak has the potential to grow exponentially until it reaches pandemic proportions.

But in reality, once people become aware that a deadly pathogen is spreading, their behaviour changes, and so does the disease’s rate of transmission.

“Once something is in the population, we’re responding not to a theoretical concept but to what we’re seeing on the ground,” Dr. Ferrari said. “That’s our effective reproduction rate.”

A simple formula for calculating the effective reproduction number, known as R, is (1 – P) x R0, where “P” is the proportion of the population that is immune.

It’s understood that R is likely to be less than R0, but in the throes of a pandemic, it’s difficult to estimate how many people are immune.

“We never have enough information to do it,” said Fred Brauer, author of “Mathematical Models in Epidemiology” and an honorary professor of mathematical biology at the University of British Columbia in Vancouver.

It isn’t known how many people in the US have been infected with the new coronavirus, but a recent study estimated that 21% of New York City residents had antibodies to the virus.

There’s no proof that people who have recovered from Covid-19, the disease caused by the virus, are protected from a second infection. But if this portion of the population was immune and the virus had an R0 of 2.5 (the midpoint of the Imperial College estimate), the effective reproduction number would be 1.98 – a figure that would still permit exponential growth of the disease.

“If you haven’t gotten sick yet, you should look at that 21% number in New York and say that it reduces your risk – but 21% of people is not 60%,” Dr. Ferrari said, alluding to another reference point, the herd-immunity threshold.

Herd immunity refers to the indirect protection afforded to people who are susceptible to a disease but unlikely to get infected because enough people are immune that transmissions have slowed or stopped.

“It’s not ‘am I immune?’” Dr. Ferrari said. “It’s ‘am I surrounded by people who are immune?’”

A simple formula for estimating the percentage of the population that needs to be immune to achieve herd immunity is 1 – (1/R0). With an R0 of 2.5, the result would be 60%.

In normal circumstances, the threshold is used as a target for immunisation coverage with a goal of protecting the population before a deadly pathogen has the opportunity to take off.

“Herd-immunity threshold is about preventing outbreaks,” Dr. Ferrari said. “It’s often misinterpreted as when an outbreak will end.”

That’s yet another concept.

Final epidemic size is the proportion of the population expected to get infected if an outbreak is unmitigated.

The formula is complex, but it predicts that, without any interventions, a disease with an R0 of 2.5 will infect nearly 90% of the population.

“An epidemic is like a wave,” Dr. Ferrari said. “As it gets bigger, it’s harder and harder to stop the wave. That’s what the epidemic final size captures. Herd-immunity threshold is about stopping the wave from ever taking off.”

As a disease progresses, researchers also try to get a handle on the expected death toll.

‘Herd-immunity threshold is about preventing outbreaks. It’s often misinterpreted as when an outbreak will end.’

Dividing fatalities by the number of confirmed illnesses produces the case fatality rate. A better estimate of lethality divides fatalities by the number of people infected. But no one knows how many people are infected with Covid-19.

“Right now the death rate is a guess,” Dr. Brauer said. “I’ve seen ranges from one-tenth of a percentage point to 3%.”

These simple formulas (and it should be noted there are more complex versions) assume that variables such as the level of social contact, a disease’s rate of transmission and the duration of infections remain constant.

But human behaviour can change the outcomes – for better or for worse.

“After superstorm Sandy, we took steps to prevent that from happening again,” Dr. Ferrari said, referring to the 2012 hurricane. “That’s the situation we’re in now. We’ve put procedures and policies in place to prevent another wave from bowling over us in the future.”

**– Write to Jo Craven McGinty at [email protected]**