World leaders and public health experts are poised to spend the coming months or years obsessed with a variable known as R0.

Pronounced “R-naught,” it represents the number of new infections estimated to stem from a single case.

In other words, if R0 is 2.5, then one person with the disease is expected to infect, on average, 2.5 others.

An R0 below 1 suggests that the number of cases is shrinking, possibly allowing societies to open back up. An R0 above 1 indicates that the number of cases is growing, perhaps necessitating renewed lockdowns or other measures.

But R0 is messier than it might look. It is built on hard science, forensic investigation, complex mathematical models — and often a good deal of guesswork. It can vary radically from place to place and day to day, pushed up or down by local conditions and human behavior.

Yet for all is vagaries, R0 is expected to shape our world in the coming months and possibly years as governments and health experts treat it as the closest thing to a compass in navigating the pandemic.

What follows is a simple guide to how this metric works, why it matters and how to think about it.

WHAT IS R0?

The term is borrowed from the study of demographics, where it is used to describe birthrates.

R refers to reproduction and 0 to the zeroth generation, as in patient zero. Together, they are typically called the basic reproduction number.

It is calculated from innate features of a disease, like how easily it jumps from one person to the next, along with elements of human behaviour that shape how often sick and susceptible people will come into contact.

The resulting number is meant to help model an outbreak’s possible trajectory.

Say that 1,000 people have a seasonal flu whose R0 is estimated at 1.3.

They would be expected to infect 1,300 people. That second generation would go on to infect another 1,690.

That can add up. By the 10th generation, about 30 days’ time, 42,621 people would have caught the flu.

But any R0 is just an estimate and, epidemiologists stress, an imperfect one.

A paper published last year in Emerging Infectious Diseases, an academic journal, described the metric as important but warned that it can be “easily misrepresented, misinterpreted and misapplied”.

There is no consensus for how to measure it. Much of the underlying math relies, by necessity, on educated guesses and on human factors that can change unpredictably.

For this reason, most diseases are given a range rather than a single figure. Severe acute respiratory syndrome (Sars) is usually described as having an R0 of 2 to 5 — an enormous difference.

Tellingly, scientists are still disputing and revising estimates for diseases that have been studied for years; R0 figures for measles have ranged from 3.7 to 203.

Still, for all its flaws, it’s useful shorthand for both experts studying the disease and leaders trying to manage it.

WHAT IS THE R0 FOR THE CORONAVIRUS?

In practice, there is no such thing as a fixed R0. It’s better to think of this number as a starting point for the virus’s behaviour in the absence of real-world human or environmental factors.

New figures are coming out all the time. But, generally, studies now estimate that the pathogen that causes Covid-19 has an R0 of 2 to 2.5.

That’s significantly higher than the flu and within lower-end ranges for Sars, another coronavirus.

To know how quickly a virus spreads, you also need its serial interval, or average time between each successive infection. Some studies estimate the coronavirus’s at 4 to 4.5 days. That’s almost twice as fast as Sars, which is why the coronavirus spreads so much more quickly.

The serial interval, though, is considered more or less fixed. People can heavily influence R0, which is why it receives so much more attention that other metrics.

A busy market ahead of a nightly curfew during the coronavirus pandemic, in Quezon City, Philippines, April 9, 2020. Photo: The New York Times

WHY IS R0 SUCH A BIG DEAL?

Governments increasingly use R0 as a metric for whether their country’s cases are growing faster than they can manage or shrinking as quickly as they’d like.

Interest in R0 has grown so intense that a video of Angela Merkel, the restrained German chancellor rarely associated with viral videos, explaining the variable has been viewed nearly 9 million times.

“We are now at about a reproduction factor of 1, so one person is infecting another one,” Ms Merkel said at press event on April 15.

“If we get to the point where everybody infects 1.1 people, then by October we will reach the capacity of our health care system.”

When a country has more patients than intensive care beds, death rates can spike drastically.

At an R0 of 1.2, Ms Merkel went on, Germany would cross that threshold in July. At an R0 of 1.3, it would happen in June.

“So that’s where you see how small the margin is,” she said.

But real-time R0 estimates like Germany’s are, however sophisticated, highly speculative. It is an estimate built on other estimates, some more informed than others.

Still, it is one of our only metrics for guessing how well lockdowns and other policies are working — and therefore for determining whether and when those policies are worth their enormous economic and social costs.

DOES AN R0 BELOW 1 MEAN THE VIRUS IS DEFEATED?

No. It means, assuming the numbers are correct, that the virus’s spread has been paused.

Where R0 drops below 1, this means that every, say, 100 sick people will infect fewer than 100 others. Each successive generation of infections will be smaller than the last.

But people can still get sick, and people can still die. It can take a long time for countries to see the virus fully recede, especially if the initial outbreak was bad.

Italy, for example, recently estimated that its social and economic restrictions had pushed the virus’s R0 down to 0.8 — a huge achievement won at a heavy cost.

How long might it take Italy to resemble South Korea, which has tentatively reopened as it confirms about 10 new cases per day?

Italy reported 15,918 new cases in five days last week, a workable shorthand for the number of people who might still be infectious. At an R0 of 0.8, it would take 26.8 generations of the virus for Italy’s new infections to pace South Korea’s.

At four days per generation, that’s about 100 days, or early August. And that’s only if the status quo — lockdown — is maintained.

Three and a half more months of social restrictions would be costly for Italy’s already-strained society and economy. And it would not be a guarantee. Even South Korea has measures in place to reimpose lockdowns if cases resurge.

This is why some experts believe that, in the coming months or years, government measures will not be aimed at simply driving down R0 as low as possible but at managing it within acceptable levels.

In such a scheme, social and economic restrictions would be lifted and reimposed in response to fluctuations in the R0. But no one knows what the right balance would be, much less how to achieve it.

A Harvard University study estimated that keeping new cases within what the health care system can manage could require calibrating off-and-on lockdowns through mid-2022.

HOW ARE GOVERNMENTS MANAGING R0?

Official efforts to track R0 are spotty but growing more common.

Several European countries now report estimates below 1, but levels of success remain uncertain.

Germany puts its own at 0.9, up from a recent low of 0.7, which had led Ms Merkel to ease restrictions. Governments face gut-wrenching dilemmas over whether to accept such upticks as necessary evils.

One study from France estimated that timely lockdowns pushed R0 down to 0.5 from 3.3, a stunning transformation.

Still, French cases jumped the day after the study was published, in part because nursing home infections had not previously been recorded, a reminder that R0 estimates are imperfect shorthand.

India, whose enormous population and rickety health care system make it one of the pandemic’s most-watched countries, estimates its R0 to have declined to 1.36 from 1.55. That’s low but still above 1 — meaning case numbers are growing.

It is difficult to assign the United States a single R0 figure. The country has multiple concurrent outbreaks, each with its own dynamics and each at a different point in its life cycle.

The former founders of Instagram set up a website that estimates state-by-state Rt values, a variation on R0 that accounts for rates of transmission. Although it is not associated with professional epidemiologists or public health experts, it has received heavy attention, reflecting the hunger for information on this useful but fuzzy metric. THE NEW YORK TIMES

ABOUT THE AUTHOR:

Max Fisher is a writer for The New York Times Interpreter, which explores the ideas and context behind major world events.