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.

The Idiocy of the “Proportional Restrictions” Approach to Fighting the Pandemic

In the previous post,I described briefly the 4 different stages of increased restrictions that Governments appear to be taking to contain the COVID virus in their countries. But what this approach amounts to is what I call as the “Proportional Restrictions Approach” – and that is what most Governments are taking up. In this approach, the restrictions imposed on the country’s population evolves directly proportional to the extent of the spread of the virus – number of infected cases and deaths.

So essentially, it is Virus Spreads first,  Restrictions come in later. With the exceptions of countries like Italy, where the outbreak happened very quickly before any meaningful measures could even be implemented, most countries are taking a ‘step by step’ approach wherein the restrictions are a direct and proportional REACTION to the increasing infected cases. So it means the Governments start by advising and suggesting people to stay indoors, then move on to declaring symbolic emergencies with no real action items, followed by restricting movement to only ‘essential’ services, but then inevitably ending with a complete lockdown of the entire country.

Simple fact is that every country all over the world which is taking this ‘proportional restrictions’ approach will inevitably reach the complete lockdown phase of restrictions in 2-4 weeks. Why? Because it is simply not possible to make humans stay home.

We humans are simply not wired to take things that we can’t see seriously. If we see a pack of rabid street dogs (or a horde of zombies) roaming the streets, we stay home. But we are completely OK heading out as long as we don’t actually see the virus or its direct impacts (a.k.a lots of sick and dead people).

So no amount of ‘suggesting’, ‘advice doling’, ‘pleading’, ‘educating’ will make mankind simply change some of the most fundamentally hardwired habits and activities within us, and make us stay at home. All over the world, there are instances where people willfully go outside for reasons that are not essential. And they will continue to do so until the Government tells them (and even demonstrates by example) that it is illegal to do so.

Which is why this ‘step by step’ or ‘proportional restrictions’ approach actually MAKES SURE that every one of those countries WILL reach a stage where the virus is completely out of control, at which point the ONLY option available is to put the country in a complete lockdown and FORCE the population to stay home. So my basic question is this:

If a country is going to a complete lockdown anyway, then why won’t they just enforce it upfront – when the number of cases are low and manageable, and when the healthcare systems actually have the resources to take care of these people?

Or put in other words, there are two options: Impose complete lockdown when you only have a small number of cases and contain the spread completely. Or impose a complete lockdown only AFTER the virus has spread sufficiently that it is no longer possible to control it with lesser measures.

As an example, here is a timeline of how New York City responded (or has still yet to respond) to the pandemic sweeping it now. Fair warning: it is a scary collection of statements and (lack of) actions from every side over the past one month. But it perfectly illustrates how the restrictions in place evolved in direct REACTION to the spread of the virus. As it stands today (March 28), the city’s parks and playgrounds are still open to the general public with the City only ‘advising’ and ‘suggesting’ that social distance be maintained. Who wants to place a bet that they will close in the coming days? Does anyone expect this to NOT be inevitable? The only difference between shutting down parks and playgrounds in early March vs early April is over 30,000 sick people and over 500 dead (with more heading that way).

So if anything, the Governments have a MORAL responsibility to shut down the country and place them in complete lockdown for 2-3 weeks with no travel into, out of or within the country. But who actually has the balls to do that?