In this post, drawing upon simple math and intuition, I will show why social distancing does not work in regard to limiting the infection of the corona virus, or its efficacy is vastly overstated. In preface, social distancing is distinct from quarantine. In the latter, individuals who are infected are required to remain in a designated/fixed location until they can no longer transmit disease; containment and social distancing is policy that restricts movement and gatherings of people to certain locations, such as preventing travelers arriving from certain countries from entering the US, or cancelling public gatherings and events. It is considered less drastic than quarantine, as it is much less restrictive to one’s freedom of movement. Or to put it more tersely, quarantine means “you must stay in location X.” Containment and social distancing means “you cannot go to locations ‘X,’ ‘Y,’ and ‘Z.'”
Over the past few weeks as the virus has exploded worldwide, many companies and organizations have canceled events, such as the NBA suspending their 2020 season , SWSX being cancelled, and Disneyland closing for a month. There is also talk of universities and schools closing. Trump ratified a European travel ban restricting entry to the US from Europe, for 30 days (which then also leads to the obvious question, that if Trump can unilaterally suspend travel from Europe to the US, why cannot he not do something about the border and suspend or severely restrict immigration from Mexico to the US too, which is what most of his voters want anyway). Regrettably, this ban is ineffective, too late, and mostly bluster to create the illusion and perception of having taken action. Given that the virus is everywhere now, he’s a month and a half too late. Stopping travel from China to the US, a month ago, in hindsight, would have been the smart thing to do. But all this does is create a major inconvenience. A day late and a dollar short, as it’s said.
Companies cancelling/closing events has become a sort of social virus intended to generate positive PR to show solidarity and awareness, similar to the trend in recent years of companies promoting breast cancer awareness. Disneyland closing for a month may hurt revenues in the short-run, but the positive press is free PR and thus from a business standpoint worthwhile in the long-run. When it reopens, there will be way above-average attendance and the public’s opinion/perception of Disney, as a brand, will have increased.
But back to the main topic, does social distancing work? Possibly a little, but much less than the media hype would suggest. I see people on either side of the aisle saying we need to close venues, schools, conferences, events, etc. for the ‘public or common good,’ but few, it seems, to have actually run the basic numbers as to what this entails in terms of efficacy.
I’m sure we have all seen the famous double bell curve graph of ‘delaying the peak’, as shown below. I think the ‘double bell curve’ is as good of an approximation of reality as a square is an approximation of a circle, which is to say it is not very accurate. People are easily swayed by such imagery without doing any further investigation or considering the possibility that it is exaggerated, similar to how drawings of the solar system are not to scale, but only a very crude approximation of the size and relative distances of the planets.
It is a convincing picture and in theory sounds reasonable, which is why it has been shared so much, but in reality, I think the second curve is much less flattened and much less delayed than we want to believe it is or that the picture would suggest. I think preventative measures such as hand washing, closing of events, hand sanitiser, etc. are much less effective than purported and media hype would suggest. That is not to say they don’t help, but they don’t help that much. Hand washing and soap are very effective against bacterium,which is why you should always wash your hands after handling raw poultry especially, but less so against tiny airborne viruses whizzing through the air and everywhere, not just on your cutlery board or on the doorknob. Shutting stuff down does not prevent prevent the virus from spreading when people merely make contact with each other in day to day settings such as on the street or at the food store. The only option is total shutdown,total quarantine, testing of everyone, which is impractical from a policy standpoint.
According to Worldmeter, as of 3/14/2020 there are a total of 2330 cases of the virus in the US, for an incidence of 7 per million. However, these people are either hospitalized, cured, or at home recovering and thus cannot easily transmit the virus. So how many asymptomatic carriers are there, which is the real concern? I have not been able to find any estimates, despite a lot of searching, or any sort of formula to extrapolate asymptomatic/incubated cases from reported cases. You would think that this info would be known given its importance, but no one seems to knows. However, after some further searching I found, according to the Daily Mail, that “half of the infected coronavirus passengers on board Diamond Princess cruise ship had NO symptoms.” So given that there are 2230 active cases in the US, based on the Diamond Princess data we can surmise that there are also an equal number of infected asymptomatic carriers in the US. However, an incidence of 7-per-million is tiny. How small? To get a visual idea, below is a stadium filled with 80,000 people. If you combined two such stadiums, assuming random distribution of the disease among the general population, one would expect just a single carrier.
Thus, shuttering an event that may only have a few thousand attendees or even a baseball game or basketball game is negligible terms of staving off infection. But doesn’t the Princess data show that people should be separated? Yes, but also the environment of a cruise ship is vastly different than a public event. The latter may last just a few hours. On a cruise ship, people are confined to the same small living area for up to weeks at a time. This means the r-naught is able to kick-in and the growth becomes exponential among this small, contained population, much like bacteria multiplying in a petri dish. Corona has an r-naught of 2.2. This is over the lifetime of a carrier and is based on an average, so some individuals may be more infectious than others. So a 3-hour baseball or basketball game, in terms of the duration of illness of an infected individual, which may last weeks, is small. And so the odds of an infected person spreading the disease two his 2.2 possible victims during this 3-hour window, are tiny. The r-naught derived from the cruise ship data is under ideal conditions for the virus, for a very prolonged period, so even under the most ideal of conditions, a carrier still manages to infect only 2 people. People have this perception that single sick person can just infect dozens at once, implying an r-naught of 100+. It’s not like that. Sometimes the virus enters the airways but dies. So this 2.2 value are based on the viruses that spread and survive long enough to cause an infection that can be detected.
Let’s assume a hypothetical asymptomatic carrier, who we shall name ‘Bob,’ is unable to go to the theater or a basketball game due to cancellations. He may instead do some other activity that puts in close contact with people, such as going to a restaurant or going shopping. Given that people attend such events sparingly compared to more mundane tasks such as shopping for food, going to work, or taking public transportation, Bob will likely infect people anyway during the course of those activities during the week or so he remains asymptomatic. Skipping the concert won’t really make any difference. The best option is for Bob to stay home or go to the hospital, limiting as much as possible the spread to other people, but this, of course, is assuming he is tested before showing symptoms. Given the shortage of testing equipment, the only people being tested are individuals with symptoms suggestive of the virus and or those who were in close contact with affected individuals.