Showing the Math
My friend Scott challenged me to “show the math” on the growth of the coronavirus based on current numbers. First, to understand the nature of the issue, I’ll quote from an article by Megan McArdle that another friend shared this morning. Here is the key piece:
“There’s an old brain teaser that goes like this: You have a pond of a certain size, and upon that pond, a single lilypad. This particular species of lily pad reproduces once a day, so that on day two, you have two lily pads. On day three, you have four, and so on.
“Now the teaser. “If it takes the lily pads 48 days to cover the pond completely, how long will it take for the pond to be covered halfway?”
“The answer is 47 days. Moreover, at day 40, you’ll barely know the lily pads are there.”
The Assumptions
The current growth rate of infections is about 1.2. We see a doubling of the cases every five days. We also know the current number of reported cases. In the world today, at the time I write this, that is 121,564. In the US it is 1,050. We also know the number of dead. #Covid, currently, has taken 4,373 lives, 31 of those in the US. The intersection of these numbers is the Case Fatality Rate or the number of deaths relative to known infections.
There is a challenge in simply dividing those numbers because 51,000 of the 121,564 cases are active. We do not know if their eventual status will be recovered or deceased. We do know that of 70,000 resolved cases, 4,373 died and 66,000 got better. That would be a CFR of 6%. All the experts assume that is not the true CFR, but they vary on estimates of what it may actually be. Estimates from near 1% to near 3.5% abound with explanations for what they seem to be.
For purposes of “the math” I am using a CFR of around 2.4 — splitting the difference between the low end of 1, and the high-end of 3.5, but hedging upward a bit to account for the current known CFR of 6.
The Math
Based on the exponential growth and the current CFR, and assuming no drastic intervention (no new medicines, ineffective control of spread through quarantine or social distancing, and people “letting life go on” without concern for spread, this is what the case numbers and fatalities in the US would look like between now and May 1.
By the first of May, 9.5 million Americans are infected and 229,000 are dead. By my birthday on May 10, just ten days later, 59 million are infected and 1.4 million are dead.
This makes a number of assumptions, not the least of which is that the numbers will grow unchecked. We know that NY has enacted a quarantine around the town of New Rochelle in an effort to stop the spread from that cluster. That type of restriction may keep the infection from spreading. Social distancing can greatly reduce the spread. So these numbers are not likely to reach those proportions. Government intervention, up to and including a complete lockdown similar to the actions in China and Italy, are likely.
But there are other things to note of a less optimistic nature. First, we actually already have 31 deaths, not 25. One of the first outbreaks was in a nursing home with an elderly vulnerable population. If the elderly are exposed more frequently, the death toll may go significantly higher. Italy, for instance, currently has 631 deaths and 10,149 known infections. I have seen some estimates that the CFR among the elderly in Italy could be 23%. An outbreak in a vulnerable population could be more deadly.
Also, these numbers make no assumption about confounding effects. For instance, look at the world numbers over the same time, if unchecked:
Within the next three weeks, the current growth trend would see 4.6 million infections. You cannot assume those numbers without assuming there will be significant disruption to availability of medical equipment and supplies. As industrialized nations shutter to ride out the disease, who will be making them? That has a direct impact on the ability to care for those infected.
So yeah, the math is pretty grim. As Megan noted with her parable, it’s still difficult to see the problem at Day 40. We are dangerously close to Day 41.