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.


It has been almost two years since there has been a new post here at the Mule, so you would be forgiven for thinking that the blog was defunct. But, I have now been prodded into action by the need to change my hosting provider.

For over 10 years a friend has very generously hosted the Mule on his servers but he is now shutting down the operation. So a big thank you to Brendan for those years of hosting.

Now that I have successfully moved the site to its new home, I will have to prod myself into action and start posting again more regularly.


Keep the date, and Vote

24 August 2017

James Glover is back with another guest post, this time digging into some poll figures ahead of the postal plebiscite on same sex marriage. Hey, there is a survey/plebiscite/referendum on, in case you haven’t heard. It’s on same sex marriage or marriage equality. Leaving aside the fact that this is a survey and not at […]

4 comments Read the full article →

May day was in June

15 June 2017

The father of the Mule is currently in  the UK and penned the following piece as he reflected on the outcome of the election. With the speed of the election cycle, the election results may already seem a distant memory, but any tardiness in publishing this post is entirely due to a slow editor (me) […]

1 comment Read the full article →

More on Brexit

19 July 2016

After observing the Brexit poll at close quarters, guest Mule contributor John Carmody travelled on to Europe and continued to reflect on the significance of the vote. In this follow-up post he reflects on the historical journey of the European Union and his reasons for thinking that the Leave vote was a terrible mistake on […]

3 comments Read the full article →


25 June 2016

Sometime Stubborn Mule contributor, John Carmody, finds himself in the UK at the time of the Brexit vote and has filed the following report. Meanwhile, back here in Australia, the Mule is watching anxiously for signs that we are on the verge of the end of Western civilisation “in it’s entirety”. On the night before the “Brexit” […]

3 comments Read the full article →

Sic Gloria in Transit on Monday

8 May 2016

Has it really been so long since there was a post here on the Mule? It would appear so and my only excuse is that I have been busy (isn’t everyone?). Even now, I have not pulled together a post myself but am once again leaning on the contributions of regular author, James Glover. From […]

1 comment Read the full article →

Direct Action

27 September 2015

It has been a very long time since there has been a post here on the Stubborn Mule. Even now, I have not started writing again myself but have the benefit of a return of regular guest poster, James Glover. This is a post to explain the Australian Government’s policy called “Direct Action”. I will […]

3 comments Read the full article →

The Role of Cycles in Charting the Unknown

23 April 2015

After penning a paper on the insidious Sleeping Beauty problem last year, Giulio Katis returns to the Mule with this guest post exploring the central ideas of The Lean Startup: How Today’s Entrepreneurs Use Continuous Innovation to Create Radically Successful Businesses by Eric Ries. Starting with the immediate application to business startups, Giulio develops to a broader view: […]

4 comments Read the full article →

Bitcoin and the Blockchain

14 March 2015

It’s hard to believe that a whole year has passed since I last wrote on the topic of bitcoin, and my remaining 1 bitcoin is worth rather less than it was back then. During the week I presented at the Sydney Financial Mathematics Workshop on the topic of bitcoin, taking a rather more technical look at […]

3 comments Read the full article →