When an infection erupts the way coronavirus has exploded in Wuhan, China, and elsewhere in the world, public-health experts try to gauge the potential for an epidemic—or, worse, a pandemic—by calculating the pathogen’s basic reproduction number.
The figure, generally written as R0 and pronounced “R naught,” is an estimate of how many healthy people one contagious person will infect. Because viruses spread exponentially, a few cases can quickly blow up to an overwhelming number. An R0 of two suggests a single infection will, on average, become two, then four, then eight.
Until the infection is contained or runs its course, the doubling will continue. But a pathogen’s basic reproduction number assumes everyone is susceptible to infection. Thanks to vaccines and other conditions, that often isn’t the case, and the effective reproduction number is lower.
When the new strain of coronavirus began to infect humans, there was nothing to slow its progression.
From One to Many
Minor differences in R0, or transmission rates, for viruses can lead to drastic differences in the number of overall infections. The new coronavirus outbreak has an R0 of 1.5 to 3.5 according to an estimate made in late January.
If four people were infected with
the new coronavirus…
…with an R0 rate of 1.5, they would
infect six more…
…who would infect nine more and so on.
But with an R0 rate of 3.5, they would
infect 14 more…
…who would infect 49 more and so on.
Because the disease, which experts have named Covid-19, is infecting humans for the first time, there is no conferred immunity from previous exposure or vaccination. Everyone can potentially catch it, and, according to the MRC Centre for Global Infectious Disease Analysis at Imperial College London, the virus has an R0 of 1.5 to 3.5.
“Right now, coronavirus is much more of a concern than SARS ever was,” said Steven Riley, a professor of infectious-disease dynamics at Imperial College, referring to the global outbreak in 2003, when 8,096 people got sick and 774 died. “The main reason is our estimate of the number of people who are currently infectious is higher than the maximum who were ever infectious at one time with SARS.”
Covid-19 and severe acute respiratory syndrome, or SARS, are both caused by coronaviruses, a family of viruses that causes infections ranging from the common cold to severe respiratory illness.
So far, China’s national health commission has reported more than 59,000 cases of Covid-19 and at least 1,300 deaths. In addition, at least 447 cases have been confirmed in 24 other countries, according to the World Health Organization, including 15 infections in the U.S.
Because many cases go undetected, the actual total is probably far higher.
Monitoring in China is likely picking up 10% or less of all infections there, according to
director of the MRC Centre. In other countries, it’s probably picking up around 25%.
“Where we’ll look next is Hong Kong and Singapore,” Dr. Riley said. “We may see a growth phase there next,” although, he added, researchers haven’t yet seen exponential growth outside of mainland China.
To estimate the potential spread, researchers at Imperial College began with two pieces of information: the time when the virus emerged, in December, and the fact that seven travelers who left Wuhan were confirmed to have Covid-19.
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To extrapolate how many other people were infected, they observed that 19 million people were in the greater Wuhan area, and on average, 3,301 traveled internationally daily.
“If you divide 19 million by 3,301, you get the per day probability of international travel,” said Dr. Riley, who was a member of the team that generated the estimate. “That’s approximately a 1 in 5,755 chance of traveling per day.”
The researchers next assumed there was a 10-day window in which an infected traveler might be detected.
“If we’ve got 10 days to detect, we’ve got 5,755 divided by 10, or a 1-in-576 chance of detecting a case,” Dr. Riley said. “You’re only going to pick up one in every 576 cases.”
They multiplied 576 cases by seven, the number of confirmed sick travelers, to come up with an estimate of 4,032 likely cases in Wuhan by Jan. 23, the end of the period they examined.
Taking the confidence bounds into account, Dr. Riley said, the figure could have been as low as 1,700 or as high as 7,800.
“Often, such a wide range doesn’t have any value,” he said. “But in this case, it’s useful because the lower bound was significantly higher than the reported severe cases.”
Based on this information, the researchers estimated the virus’s growth rate and assumed that, like SARS, an average of 8.4 days elapsed between the time one person caught the virus and then infected others—what is known as the generation time.
“If you know how fast it’s growing and the average time between generations, you can say what is the average number of offspring each case has,” Dr. Riley said.
They concluded the number ranged from 1.5 to 3.5, or a central estimate of 2.6.
To control the virus, they estimated that more than 60% of transmissions need to be blocked.
At this stage, it’s too soon to tell how well quarantines and other interventions are working, but experts expect the infections will continue to spread.
“I think it is likely we’ll see a global pandemic,” said Marc Lipsitch, a professor of epidemiology at Harvard T.H. Chan School of Public Health. “If a pandemic happens, 40% to 70% of people world-wide are likely to be infected in the coming year. What proportion of those will be symptomatic, I can’t give a good number.”
Write to Jo Craven McGinty at Jo.McGinty@wsj.com
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