The Brutal Math Behind Flattening the Curve

  1. Delayed onset
  2. High rate of hospitalizations
  3. Exponential growth

Delayed Onset

The most insidious thing about coronavirus is that you are infectious even before you show any symptoms. You may not know you are infected yet, but you can still transmit it to your friends and family (or strangers, of course). This means that we have to be super proactive in preventing transmission before people show any symptoms. If we wait too long, until many cases start showing up in hospitals, like Italy did, it’ll be too late. Notably, Taiwan is right next to China, but they immediately went into action before the WHO even recognized coronavirus as a threat²; they were able to keep it contained. Italy dragged their feet until it was obvious, and by then it was too late³. Fingers crossed that the USA didn’t wait too long, but because symptoms don’t show up until later, we won’t know for a couple weeks.

High rate of hospitalizations

But then the question becomes: is it actually so bad? We already deal with things like seasonal flu every year. Well, roughly 84%⁴ of coronavirus cases are not that bad. You might not even know you have it, but for many people it’ll just be between a bad case of flu and a mild cold.

Exponential growth

Luckily, if people don’t get sick at the same time, we can reuse equipment. But this is where the final whammy hits us. Coronavirus is a new disease, which means that it has the power of exponential growth. As a math professor, I make no apologies now for giving you a word problem and taking you back to high school math class. Imagine a large pond that is completely empty except for 1 lily pad. Each month, the lily pad doubles, so there are 2 lily pads in the second month, 4 in the third month, etc. Let’s say that the pond has about 1 million lily pads after 20 months. When did the pond have half a million lily pads? The answer is after 19 months. Because of the doubling property, the newest half a million lily pads all were added in the last month.

A fighting chance

Even if we can’t get the effective reproduction number to below 1, lowering it still helps a lot. A reproduction number of 2 is terrible, because it means that half of all cases ever are happening right now, and twice as many as the previous week. A reproduction number of 1 would mean that the number of cases is steady every week, which is all right, because then our health-care system can easily keep up. But even lowering that number a bit helps a lot because it means fewer simultaneous cases that hospitals have to deal with, and with the various states of emergency that have been declared, we can put in more resources to the medical system to help with the increased load. This is the math behind the drive to #flattenthecurve.

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Yun William Yu

Yun William Yu

Assistant Professor of Mathematics, University of Toronto // https://yunwilliamyu.net