COVID-19 Projections
United States, US/Washington, US/Texas, US/New York, US/Florida, US/California, US/Arizona, United Kingdom, Turkey, Thailand, Switzerland, Sweden, Spain, South Korea, Saudi Arabia, Portugal, Poland, Pakistan, Norway, Netherlands, Malaysia, Luxembourg, Japan, Italy, Israel, Ireland, Iran, Indonesia, Iceland, Greece, Germany, France, Finland, Ecuador, Denmark, Czechia, China, Chile, Canada, CA/Quebec, CA/Ontario, Brazil, Belgium, Austria, and Australia
What do these plots show?
These plots show the cumulative number of people confirmed to be infected with SARS-CoV-2 virus or dead as a result of COVID-19 disease. The number of people recovered is not shown because including them makes the plots visually confusing.
Because these are cumulative counts, they never go down. Fortunately, when the lines flatten out it means that no new new infections or deaths are being reported. Death counts are likely to be vastly understated because death is often a result of unconfirmed SARS-CoV-2 infection or as an indirect consequence of COVID-19 disease.
Remember, testing for SARS-CoV-2 is very sporadic. So the population counts are confounded with both the availability of testing kits and strongly-regional policies about who gets tested at what time for what reason. So both “confirmed” and “deaths” counts are likely vaslty understated, with the death count being even more artificially low than the “confirmed” case count.
This is so important that it’s worth restating. The lack of pervasive, systematic testing, in the United States as well as elsewhere, make these numbers erroneously optimistic, and nobody knows if that optimisim is only a little-bit wrong or if it is hugely wrong.
That’s why testing, which is missing in much of the world, is so important.
The curves show the best-fit exponential growth model which estimates both how quickly we expect to see new occurrences, under the hopefully-incorrect assumption that we are nowhere near the end of the pandemic. The exponential growth model is more appropriate when we have discontinued physical distancing since, under that scenario, transmission of SARS-CoV-2 is considerably more rapid and can theoretically infect everybody, in an “infinite population” sense.
Notice that discontinued physical distancing gives much more pessimistic population counts than the alternate, more optimistic logistic growth scenario!
How do I interpret the plots?
We draw a solid line throught the most recent (rightmost) data points. In most cases, the straight line fits those points very well. That straight line represents “pure” exponential growth in the number of COVID-19 cases. If you project that straight line one or two weeks into the future the numbers that get predicted can be startlingly large.
Now it is true that in some cases, for example Italy, where the long-term trend shows more of a curve than a straight line. That shows that the rate of disease spread is decreasing, which is a good great thing. A [more complex model][logistic.md] would have you draw a curve through the points and continue on up. But note that regardless of whether the future trend is a straight line or if the line flattens out, exponential growth guarantees that a great many more infections and disease cases are, to some extent, inevetable.
Further Background
A wonderful, well-rounded primer has been written by Ars Technica.
The Internet is full of dire warnings about the upcoming surge of SARS-CoV-2 infections. Article after article after article warn of a huge and sudden increase in SARS-CoV-2 infections. For most of us, the “exponential blow-up” of the pandemic must ultimately be taken as a matter of faith.
There are already several easy-to-understand, non-mathematical, and more-mathematical online explanations of disease transmission and the growth of epidemics. But I wanted to make things even simpler, and remove some of the “mathematical magic” behind the dire pandemic predictions. And the simplest thing I could think of was plotting some points and drawing straight lines.
The trick is to scale the number of cases by “order of magnitude”. We know that 1,000 people is ten times the magnitude of 100, and we know that 10,000 people is ten times the magnitude of 1,000. And it turns that if we plot the magnitude of covid-19 infections over time, it is easier to understand how the epidemic is behaving. We can use the past behavior to predict the epidemic will likely behave in the future.
So simply plotting the data and looking at it should be enough to convince almost anyone that we should be very worried indeed. Especially since our population counts are likely vast underestimates.
So before reading too much into these plots, please read or skim the following articles:
- America’s COVID-19 testing has stalled, and that’s a big problem
- Coronavirus Case Counts Are Meaningless
- Unless you know something about testing. And even then, it gets complicated…
- Why It’s So Freaking Hard To Make A Good COVID-19 Model
Statistical Details
The population counts were fit via weighted ordinary least squares in “log” space to a
\[\log_2\left(n\right) = \beta_0 + \beta_1\cdot t\]model, where \(t\) is the time in days and \(n\) is the number of people. The number of days used to fit the model parameters was chosen by inspection. The same number of days were used for all countries and populations, and is depicted on the plots by the solid line interpolants.
After a lot of inspection and haggling with statistician and biologist colleagues, a simple linear weighing scheme was chosen to reflect the fact that more recent observations really should be granted slightly more evidentiary weight than those in the past. As with all hyperparmeter tuning, the devil is in the details, so… caveat emptor.
Acknowledgements
Special thanks to Johns Hopkins University and the ESRI Living Atlas Team for providing the world with such a valuable resource. Like almost every analysis online, this work was based on the JHU CSSE Data.
United States state-level data is generously provided by the New York Times.
Kudos to GitHub for supporting Open Source software and research!
This site is generated from https://github.com/adfernandes/covid19 by automated actions.
Copyright © 2021 by \({\sfst Andrew\ Fernandes\ \langle\email{andrew}{\scriptsize @}{fernandes.org}\rangle}\).