Turning the Tide on COVID-19
On the typical trajectory of the COVID-19 pandemic and how to spot changing growth rates.
Lightly edited based on new data available on 30/30/2020
Over the last few days and weeks the coronavirus pandemic has produced a veritable tsunami of data, statistics and graphs, as the disease’s progress is meticulously measured while it makes its way around the globe. One of the most common graphs we have seen depicts the dreaded exponential growth curve, by plotting the total number of cases against time to emphasise how quickly the coronavirus is spreading; see here for some examples. But what if we want to detect whether or when the rate of infection is slowing? Such graphs are less well-suited to this, and it can be hard to spot the early signs of change.
A defining feature of exponential growth is that the number of new cases depends on the number of existing cases. This relationship is relentless and notice that it is independent of time; it doesn’t matter whether we measure in hours, days or weeks, in March, April or May.
If we plot the number of new cases against the (cumulative) total number of cases, then we get a straight line. This is what we have done below, for countries with at least 100 confirmed cases, using a log axis for both the new cases and the total cases; the new cases data is smoothed using a 5-day rolling average. The tangle of grey lines, visible in the background, corresponds to the virus’s trajectory countries with at least 100 cases. The coloured lines highlight a subset of these countries; each marker on these lines corresponds to a new day. For the most part we can see how countries all follow more or less the same straight-line pattern, signalling exponential growth.
One of the most useful features of this chart is that it helps to emphasise countries that depart from this trajectory, as they start to contain their outbreaks. For example, China and South Korea standout because they have departed from the straight-line trajectory of exponential growth. I like to call this a drip-chart, because the traces for these departing countries appear like drips of paint running down the page.
Other countries — Japan, Singapore, Qatar, Denmark, for example — have at least been able to slow their outbreaks, although it is somewhat worrying that over the past few days they seem to be heading back towards the exponential growth path. Ireland, where I am, began to curtail movement and about 2 weeks ago and it too seems to be moving away from the worst-case path, although it is surely too early to be confident of this.
In Europe, the UK, France, Germany, Spain, and of course Italy, continue to struggle with the relentless growth of the disease. In Italy we might be seeing some tentative signs of improvement. The number of new cases has remained stable for almost a week now — see the magnified insert in the graph below — which, in other countries (e.g. China), has been a pre-cursor to a phase of more robust containment. If this is the case then hopefully Italy will shift to similar trajectory to that followed by South Korean or China in the coming days.
Unfortunately the US looks to be struggling because virus remains on the exponential growth path leaving the US with more COVID-19 cases than any other country. Moreover, it has achieved this dubious status in record time — the larger gaps between the daily markers on the US line indicate that things have been changing rapidly on a daily basis — and, unfortunately, there are no signs that the US will depart from this trajectory any time soon.
Of course all of the usual caveats apply, especially given that it is all but impossible to disentangle changes in the growth rates of new cases from changes in testing programmes.
Below is a similar visualisation but for deaths, rather than confirmed cases. It shows a similar pattern, but the situation in Italy, Spain, France, and the US is set in even starker relief against the comparative success of China.
And, just for good measure here are two sets of graphs showing the trajectory of each of the countries in our dataset that have more than 100 cases (or 10 deaths) in terms of new daily cases/deaths versus total cases/deaths.
For more information …
The above analysis is based on a daily COVID-19 dataset produced by the European Centre for Disease Prevention & Control. I am trying to maintain a listing of related datasets in another blog post. All code and data can be found on GitHub and new posts will be uploaded to Data in the Time of Corona on Medium.
