Which COVID-19 Curve Should We Flatten – New Cases, Total Cases, or Active Cases?

The most common talking point on the Covid-19 pandemic has been the idea of ‘flattening the curve’. It generally refers to the idea of taking measures to reduce the number of cases in any given geographical area over time. The ultimate objective is to ‘spread’ the infections (pardon the pun) over a period of time while simultaneously reducing the number of people who are getting infected. This is expected to have the desired effect of lessening the burden on the healthcare systems and to also reduce the overall number of people who would get infected over the lifetime of the pandemic.

ftc
Flatten The Curve – But What is on the Y-Axis?

We have all seen the standard ‘Bell Curve’ as an illustration of this idea. A steeper and higher bell curve (albeit over a shorter duration) is what is to be avoided  as this would indicate a large fraction of the population getting infected over a short time. Instead, the objective is to achieve a flatter and lower bell curve that lasts longer as this would mean a lower fraction of the people infected, but over a longer time. The X-axis (horizontal) in these charts is obviously Time. But where the discrepancies and confusion sets in, is what exactly is plotted on the Y-axis. To be specific, is it ‘Daily New Cases’, ‘Total Cumulative Cases’ or ‘Active Cases’? Is there anything that is correct and incorrect, or is it just a matter of interpreting data differently?

To be clear, it is completely acceptable to simply plot any of the three data sets on the Y-axis and show the resulting chart as a general attempt to provide information. But when one uses the phrase ‘flatten the curve’, the question then is which one should be plotted on the Y-axis?

SKorea chart
Daily New Cases vs Total Cumulative Cases

My personal preference is to plot Daily New Cases to get a proper picture of the scenario. I also believe this is what the original ‘flatten the curve’ referred to. The information in this chart and its interpretation is pretty straightforward. Over time, the number of Daily New Cases goes up, maxes out, then slowly decreases until it reaches zero – at which point the virus is eradicated. At a given point in time, the chart shows where a country stands in this overall trajectory. If it is going up, we know the rate of infections is increasing, and vice versa. If you want the total number of cases at any point in time, all you have to do is add the Daily New Cases for each day till that point – or as the basic definition of an INTEGRAL goes, you simply calculate the area under the curve. So the use of the phrase ‘flatten the curve’ and all its implications (as outlined earlier in this post) perfectly correlate with the Daily New Cases on the Y-axis.

Now how about the Total Cumulative Cases?  By Total Cumulative Cases, I simply mean the total number of infections from the time the first case was reported. Very importantly, it DOES NOT take into account the number of recoveries or the number of deaths. So what this means is that the curve of the TOTAL Cumulative Cases, by definition, only increases till the time there are no new cases at all – at which point, it becomes a horizontal line with the final Y-axis value equal to the TOTAL number of people who were infected at one time or the other. (See above chart)

So is it correct to use the phrase ‘flatten the curve’ while referring to this chart? The short answer is NO, this is incorrect. Firstly, this curve will never ever go down. After an initial increase in steepness (slope increases), it will simply become lesser and lesser steep over time (slope decreases) until it becomes horizontal (slope of zero). But this will never ever go down (slope never becomes negative). So it is completely incorrect to use the phrase ‘flatten the curve’ while plotting the Total Cumulative Cases on the Y-axis. Yes you can still technically state that the curve as such is ‘flattening’ but that would only imply a reduction in the slope of the curve but with a lower bound of zero.

SKorea chart2

And finally, we come to Active cases. I have not actually come across any article which shows a chart with Active Cases plotted on the Y-axis to illustrate the phrase ‘flattening the curve’. But this is actually a legitimate chart that can illustrate the idea of flattening the curve in a different manner. By Active cases, I am counting the total number of people at any given point in time who have been diagnosed with COVID-19 and WHO ARE STILL DEEMED TO CARRY THE VIRUS. So this is essentially the Total Cumulative Cases reduced by the number of people who have ‘recovered’ and number of people who have died. At any point, the number of Active Cases will always lie BETWEEN the Total Cumulative Cases and the Daily New Cases.

It will never reach as high as the Total Cumulative Cases and it will always stay above the Daily New Cases. It will reach its peak before the Total Cumulative Cases curve becomes horizontal, but definitely AFTER the peak of the Daily New Cases. (By the way, the peak here refers to the point the number of daily recoveries and deaths exceed the number of daily new cases). It will ultimately go to zero long after the Daily New Cases has gone to Zero. So in a way, this Active Cases curve also shows the same properties of the Daily New Cases curve. It can also track the rate at which patients are recovering and/or dying. As a result, all the implications and messaging from the usage of the phrase ‘flattening the curve’ correctly applies to the Active Cases curve as well.

To summarize, it is completely acceptable to use any of the three data sets to plot over time to provide general information. But the phrase ‘flatten the curve’ should only be used when plotting either Daily New Cases or Active Cases. It should NEVER EVER be used when showing a chart that plots Total Cumulative Cases over time. If you find anyone doing so, please feel free to point it out.

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