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The math behind why we need social distancing, starting right now

How just one case of coronavirus could lead to thousands more if we all don’t limit social contact.

Health officials and citizens in the United States and Europe are desperately trying to slow the spread of the Covid-19 coronavirus outbreak and are pleading with each other to practice social distancing and good hygiene.

Canceling events and family gatherings, closing schools, and reducing visits to public spaces and businesses are simple, powerful, and effective tactics to control disease transmission alongside testing to identify sick patients and isolate them from others.

And since the novel coronavirus is already spreading locally in several communities, epidemiologists say measures to limit the spread of Covid-19, the disease caused by the virus, are most effective right now in the early stage of the outbreak, when few people are infected and the most lives can be saved. Conversely, the disease becomes vastly more dangerous the longer the country waits to implement such measures, particularly since it can spread even before an infected person shows symptoms.

Countries like China and Italy found this out the hard way when they, seemingly overnight, experienced massive increases in the number of Covid-19 infections and deaths.

The math behind the outbreak explains why.

Right now, many places seeing Covid-19 transmission are following an exponential growth trajectory. That is, the rate of the spread of the infection is proportional to the number of people infected. Each infected person is expected to infect a certain number of people — around 2.5 right now — who each in turn go on to infect 2.5 more, and on and on, unless drastic measures are taken to reduce social contact and isolate the infected from others.

Think about counting doubles — 1, 2, 4, 8, 16 and so on. How many times would you have to double to get to more than 1 million? 20. How many doubles to get to more than 16 million? 24.

So that’s why Covid-19 appears to spread very slowly, and then all at once.

As epidemiologist Adam Kucharski pointed out on Twitter, this trend also shows how important it is to reduce the rate of infection early.

And individual actions can make a big difference. Reuters showed how one Covid-19 patient in South Korea, so-called Patient 31, had direct contact with 1,160 people and created new clusters of the infection. The lesson: Don’t be Patient 31.

Of course, Covid-19 can’t spread exponentially forever. There are upper limits to the population and over time, people start to build immunity to the disease and the infected start to recover, so there’s a natural ceiling. As with many other disease outbreaks, there will likely be a peak and decline in the number of cases.

Nonetheless, it’s important to lower that peak and spread out the cases as much as possible. That buys valuable time for health providers, allowing them to acquire the tools they need like beds and ventilators while avoiding being overwhelmed by patients. Flattening the curve of cases over time can therefore save lives, and in places where the health care system is already close to capacity, it’s critical.

An infographic that shows the goals of mitigation during an outbreak with two curves. The X-axis represents the number of daily cases and they Y-axis represents the amount of time since the first case. The first curve represents the number of cases when no protective measures during an outbreak are implemented and displays a large peak. The second curve is much lower, representing a much smaller rise in the number of cases if protective measures are implemented. Christina Animashaun/Vox

Taking drastic measures to limit the transmission rate of Covid-19, like closing schools, canceling public events, and sending people home from work, may seem like an overreaction when few people in a city or state are infected. However, early in the outbreak is exactly when such measures are most effective.

Using data from Hubei province, China, where the virus originated and where the vast majority of the Chinese cases were seen, designer Tomas Pueyo posted on Medium a conceptual model he created showing the difference even one day of social distancing can make in reducing the burden of cases. Vox has recreated the chart here (note that this is based on a theoretical model and not actual reported figures):

Christina Animashaun/Vox

According to an epidemiological model visualized by the New York Times, one scenario is with no interventions, the number of infections in the United States reach 9.4 million. But with aggressive public health interventions starting today, that peak could fall to 3 million, according to the model. So the sooner such measures start, the bigger impact they will have.

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