Mar 29 JDN 2458938

It could be given as a story problem in an algebra class, if you didn’t mind terrifying your students:

A virus spreads exponentially, so that the population infected doubles every two days. Currently 10,000 people are infected. How long will it be until 300,000 are infected? Until 10,000,000 are infected? Until 600,000,000 are infected?

The answers:

300,000/10,000 is about 32 = 2^5, so it will take 5 doublings, or 10 days.

10,000,000/10,000 is about 1024=2^10, so it will take 10 doublings, or 20 days.

600,000,000/10,000 is about 64*1024=2^6*2^10, so it will take 16 doublings, or 32 days.

This is the approximate rate at which COVID-19 spreads if uncontrolled.

Fortunately it is not completely uncontrolled; there were about 10,000 confirmed infections on January 30, and there are now about 300,000 as of March 22. This is about 50 days, so the daily growth rate has averaged about 7%. On the other hand, this is probably a substantial underestimate, because testing remains very poor, particularly here in the US.

Yet the truth is, we don’t know how bad COVID-19 is going to get. Some estimates suggest it may be nearly as bad as the 1918 flu pandemic; others say it may not be much worse than H1N1. Perhaps all this social distancing and quarantine is an overreaction? Perhaps the damage from closing all the schools and restaurants will actually be worse than the damage from the virus itself?

Yes, it’s possible we are overreacting. But we really shouldn’t be too worried about this possibility.

This is because the costs here are highly asymmetric. Overreaction has a moderate, fairly predictable cost. Underreaction could be utterly catastrophic. If we overreact, we waste a quarter or two of productivity, and then everything returns to normal. If we underreact, millions of people die.

This is what it means to err on the side of caution: If we are not 90% sure that we are overreacting, then we should be doing more. We should be fed up with the quarantine procedures and nearly certain that they are not all necessary. That means we are doing the right thing.

Indeed, the really terrifying thing is that we may already have underreacted. These graphs of what will happen under various scenarios really don’t look good:

But there may still be a chance to react adequately. The advice for most of us seems almost too simple: Stay home. Wash your hands.