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Coronavirus math shows why social distancing is key to reducing exposure

If transmission is cut by 75%, new infections will subside, eventually stop

By Marie McCullough, The Philadelphia Inquirer
Published: March 26, 2020, 6:04am

PHILADELPHIA — If you still doubt the crucial importance of avoiding other people, or if you think “stay at home” orders are excessive, consider this:

Without the lockdown in Wuhan, China, where the pandemic started, there would have been 44,214 cases in other Chinese cities through February — instead of the actual number of 27,956, according to a new study led by University of Pennsylvania economist Hanming Fang.

“Social distancing and, if an epicenter can be identified, as was the case for the city of Wuhan in China, a lockdown can play crucial roles in ‘flattening’ the daily infection cases curve, giving the stressed medical system a chance to regroup and deal with the onslaught of new infection cases,” wrote Fang and his co-authors.

“Flatten the curve” has become a rallying cry, but in New Jersey and New York, it appears to be too late. In both states, the average daily rate of increase is more than 50 percent, according to an Inquirer analysis of data from Sunday. As a trickle of patients has turned into a deluge, New York City hospitals are scrambling to find more ventilators and protective gear, and New Jersey is moving to reopen the former Inspira Medical Center Woodbury as an intensive care facility.

In Pennsylvania, which has 644 reported cases, the tally is increasing at an average daily rate of 34 percent. Though lower, that’s still a growth trajectory that will lead to an overwhelming surge in patients needing hospitalization.

Drawing on worldwide data, University of California, San Diego biologist Robert A.J. Signer and art director Gary Warshaw created a graphic that conveys the effect of reducing exposure to the virus through social distancing.

Here’s their math: Symptoms of the illness develop on an average of five days after infection. During those five days, called the incubation period, the virus can spread. If the rate of spread is the same for those with and without symptoms, then one infected person transmits the virus to 2.5 other people on average, and those 2.5 people each transmit to 2.5 more people, and so on. Within 30 days, 406 people would be infected.

Social distancing that reduces interaction by 50 percent would halve the chances of spreading the virus, so one person would only infect 1.25 other people on average, and there would only be 15 infected people in 30 days, Signer calculated.

But if people stay home and transmission is cut by 75 percent — so that an infected person spreads the disease to less than one other person on average — new infections will eventually subside and stop. That’s what has happened in Wuhan, where the 50-day lockdown is being eased.

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