COVID-19 data

by Stubborn Mule on 21 March 2020 · 7 comments

There is no shortage of commentary on COVID-19 online and off. There is also an abundance of data available, which is as good a reason as any for the first Mule post of 2020.

One of the best data resources online is the Johns Hopkins dashboard created by the Center for Systems Science and Engineering (CSSE). For those interested in performing their own analysis, the CSSE has also made the underlying data available in a Github repository.

It has become commonplace to refer to the “exponential growth” of the disease. For many, this is just short-hand for “really” fast. Others may recognise an exponential curve in the charts below, with the exception of South Korea.

Confirmed COVID-19 cases

However, displaying the case data in this way does not give a very clear picture of what is actually going on. A better way to display the data (New York Times) is to use a logarithmic scale. In these charts, the values on the vertical axis increase exponentially (the labels here are successive powers of 10) and pure exponential growth would appear as a straight line. Of course, the real world is never pure, so the COVID-19 data do not appear straight lines, but for a number of countries – including Australia – there are periods where it comes very close.

Confirmed COVID-19 cases (log scale)

When plotted on a logarithmic scale, the slope of the line corresponds to rate of growth. In late February, the slope of the curve for South Korea turns sharply up, as the number of cases exploded, only to flatten again as drastic measures began to slow the growth rate. In contrast, the slope of the curve for the USA is becoming steeper – disturbingly the rate on growth in confirmed cases is increasing.

To get a better sense of these growth rates, the charts below show the daily growth rate in confirmed cases. The data is noisy, so smoothed curves are added to give a sense of the trend. In mid-February, the number of confirmed cases was growing extremely rapidly. As containment measures were introduced, the growth rate was quickly reduced, but not before cases had reached the thousands. After that, the gains became harder fought and, while the growth rate is still falling, but only slowly and is currently around 12-13% daily. In contrast, South Korea has managed to bring its growth rate down to only 1%.

Growth rate of confirmed COVID-19 cases

Although the case count in Australia is still only in the hundreds, it is growing at a similar rate to that seen in Italy in mid-March. Confirmed cases inevitably lag actual cases, as detection takes time, and as a result there will be a lag in the impact of any containment measures. So, it is too early to tell how much impact the recently imposed travel and social distancing restrictions will have.

Everyone will be hoping these measures will help, but if they do not and the current growth rate persists in Australia, the confirmed case count in New South Wales will be over 7,000 in two weeks, around 30,000 in three weeks and heading towards 200,000 in a month. The prospects in the USA look scarier still: there are already over 5,000 cases and the daily growth rate is around 30%. If that rate doesn’t slow, in a month there will be around 50 million confirmed cases.

Here is hoping those log scale curves start to flatten.

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{ 7 comments… read them below or add one }

1 Dan March 21, 2020 at 10:12 pm

Great to see you back Mule. So so sad it had to be for this.

2 MarkL March 22, 2020 at 12:35 pm

Welcome back, Mule! Just what we need to get us through the approaching lockdown (hopefully to start sooner rather than later).

3 Bruce Kelley March 22, 2020 at 12:46 pm

it is great to see you back. this post is excellent for some of us who have been a long time outside the mathematics curriculum., I hope to see more in the future.

4 Stubborn Mule March 22, 2020 at 4:31 pm

@MarkL @Dan – thanks and hi. Looks like the shutdown starts Tuesday

5 Camelia March 22, 2020 at 11:26 pm

Glad to read you again! Unfortunately, we’re only 18 days behind Italy… I played with the same logscale, scaling by millions of habitants and shifting Aus and NSW by -18 days. Spot on Italy’s curve… I’d say it’s no time for half measures, still…

6 Camelia March 22, 2020 at 11:56 pm

Glad to read you again! Unfortunately, we’re only 18 days behind Italy… I played with the same logscale, scaling by millions of habitants and shifting Aus and NSW by -18 days. Spot on Italy’s curve… I’d say it’s no time for half measures, still…

7 Stubborn Mule March 31, 2020 at 10:26 am

Fingers cross we now seem to be slowing!

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