Given the mathematical nature of this website I feel reluctantly impelled to address the coronavirus pandemic. The mathematics behind the spread of infection is basically the same exponential growth that I discussed in the “Math and Religion” post and has recently been explained by the ever-lucid Grant Sanderson at his 3Blue1Brown website.
What I wish to draw attention to is the series of posts on the coronavirus by Kevin Drum on his website at Mother Jones. I have collected his recent posts comparing the spread of the virus in various countries and added some mathematical commentary of my own, which is the content of this post.
But the bottom line seems to be that in virtually all the countries, including the US, the virus infection is spreading at the Italian rate of doubling every 4 days! The readers of this website are sufficiently numerate to realize the frightening import of that number. If that weren’t enough, Kevin provides additional posts on the results of the modeling at the Imperial College that are truly nerve-wracking for someone such as myself in the most vulnerable cohort. The only blessing so far seems to be that, for once, the children are spared.
At this time, I don’t have the stomach to keep updating the post as new numbers come in. That may change. I could address the catastrophe of having ignorance and incompetence at the helm of the national ship of state, but it is too depressing.
See the Coronavirus Mathematics
(Update 3/17/2020, Update 3/21/2020, Update 4/17/2020)
(Update 3/17/2020) That didn’t take long. But Kevin Drum had an update to his curves that I thought was relevant, so I have included it in a revised version of his posts. He is also saying his plots show a 5-day doubling rate instead of the 4-day that I had determined—infinitesimal consolation.
(Update 3/21/2020) Kevin Drum had a significant update regarding the mathematical model for the growth of the infection. It is not ultimately exponential or even logistic. Contrary to religious conversion, which is essentially permanent, infections go away when the subject either is cured (likely) or dies (less likely). So the ultimate shape of the curve is closer to a Gaussian distribution.
Coronavirus Growth in Western Countries: March 18 Update
Kevin Drum, March 19, 2020
Here’s the coronavirus growth rate through Wednesday. The US is now slightly above the Italian trendline, possibly because we’ve picked up the pace of testing.
A couple of notes. First, a friend emails to warn me against calling the spread of coronavirus “exponential.” Technically, that’s true. At the beginning of a viral outbreak the growth rate is pretty much exponential, but it slows down later. This article suggests that it then follows a power law, and eventually it flattens out and then declines. When all’s said and done, the outbreak will follow a Gaussian path that looks like a familiar bell curve. For example, here is the growth curve of the Spanish flu in 1918, skyrocketing from nothing to massive death tolls over the course of only four weeks:
(Update 4/17/2020) After my previous postings, I would hope you are continuing to monitor Kevin Drum’s excellent updates and discussions. I would like to mention a different mathematical take on the situation, namely, simulations. Grant Sanderson at his excellent 3Blue1Brown Youtube blog (3/27/2020) has a marvelous epidemic simulation using a simple SIR model that illustrates the effects of
- Basic Setup (growth rate sensitive to # daily interactions, probability of infection, duration of illness)
- Identify and isolate
- Social distancing
- Travel restrictions
- R (effective reproductive number: #expected new infections by infected person during illness)
- Central hubs (periodically visit grocery store, etc.)