What does “flatten the curve” really mean?

One of the most common phrases we hear of late when discussing about the Coronavirus disease (COVID-19), is that we must try our best to flatten the curve. While this is true, many people don’t understand the reason why. It is important to manage our expectations about where we are, and what’s coming, and that’s what I will try to show in this article.

I will try to show that:

  1. We need to flatten the curve
  2. Most of us are going to get infected anyway

The curve

This is the curve many have seen:

I wrote a simulation using real data from USA as of today (SIR model). And as you can see it resembles the “flatten the curve” graphs you might have seen before.

USA model simulation

However, what you don’t see are the magnitudes; 12,000,000 people in the worst case scenario, and 3,000,000 people in the best. This Y axis is the number of active cases at any given day, provided that 50% of the cases are not noticeable, and only 15% might need hospitalization.

The total number of active cases would be 164,000,000 in the worst scenario, and 40,000,000 in the best.

And the time span is one year. The peak of the worst scenario would be at day 78, and in the best case scenario that day there would be 30,000, so sure; 30,000 is better than 12,000,000, but the true objective of flattening the curve is to delay the peak, which would happen at day 240 instead of 78.

So yes, it’s good to delay the peak from day 78 to day 240, and to reduce the active cases that need hospitalization from 12,000,000 to 4,000,000, so social distancing is good, but that will not be enough; the healthcare system will still be overwhelmed, and people will die as a result.

Healthcare limit

The totals

However, one thing is the number of active cases, which doesn’t look very good, another is the total number of cases.

Active cases
Total cases

In the worst case scenario there would be 326,000,000 cases, and in the best case 250,000,000. So to think that you will not get infected if everyone performs social distancing is delusional.

This is why experts say 70%-80% of the population will get infected (76% in this case) (even in the best case scenario).

So this is the actual curve people should keep in mind:

Active vs. total cases

The numbers

The difference in my model between the worst case scenario and the best, is the growth factor (worst: 1.2, best: 1.04), but what does that number mean?

If yesterday the total number of active cases was 32,859, and today they are 43,112 (as of 2020-03-23), that means dividing today by yesterday you get 1.312 (32,859 * 1.312 = 43,111). Is this good or bad?

Right now South Korea is 0.98, and Italy is 1.07, so yeah, 1.312 is pretty bad, so bad in fact that it’s 10% worse than my worst case scenario, and the worst case scenario is 15% worse than the best. When the growth factor is 1.0 that means the curve is at its peak; South Korea presumably has passed it already.

When people say “flatten the curve” what they really mean is reduce the growth factor; when you reach 0.0 the curve is flat.

Imagine you are in a car, and the accelerator pedal is stuck; not only will you be moving forward, you will be moving forward with an ever increasing speed. Surely you wouldn’t feel safe until the accelerator is unstuck, and that is the inflection point; the point in which the velocity stops increasing.

It’s easier to see the two points by visualizing the new cases per day (velocity); the point in magenta is the inflection point (deacceleration), the blue one is the top of the curve.

When you visualize the total number of cases the inflection point is different, and when reached you should expect the total number of cases to be twice as they are at that point.

The important thing to note here is that as long as no inflection point is reached, the growth is exponential, and there may be many orders of magnitude to go, so basically there’s no end in sight.

Where are we?

Have we reached an inflection point? The short answer is: we can’t say yet. There’s too much day-to-day volatility, and conditions in every country are drastically different.

USA growth factor rolling average

As you can see USA not only is in bad shape, but it’s getting worse; the graph should be moving closer to 1.0, not away.

Growth factor rolling average

Fortunately not every country is in the situation of USA; some countries are getting significantly closer to 1.0, even though not quite there yet.

World growth factor rolling average (except China)

Worldwide we are all over the place.

I think it’s safe to say we are nowhere near any inflection point.

But wait

Say that somehow miraculously we reach an inflection point and we are on our way to a perfectly flat curve. Can we be content now?

Well, no, the virus can make a comeback, depending on the seasons, or even mutations. The Spanish flu of 1918 did in fact do so; the second wave was much deadlier than the first, and it wasn’t the last one.

Spanish flu waves

Even in the most ideal of situations like in South Korea, the nature of a pandemic makes it so not any country is “safe” until the whole world is safe; the virus can be reintroduced into the country, in fact, many times over.

As a simplification you can think of the world as a neighborhood. You can choose to stay home and delay the inevitable, but if everyone else is infected you will eventually be too, unless you stay inside for years.

The solution

The only realistic solution (other than let things run their natural course) is vaccination, but as of today no vaccine is expected in less than 18 months.

So we can try to delay the worst by social distancing, closing airports, and pretty much everything you can think of, and we may be able to delay the worst (reduce the growth factor to less than 1.04), but even so it might not buy us enough time for the vaccine.

Conclusion

It’s too soon to tell where we are and where we are heading. Many of the parameters needed to make reasonable predictions are not known with any real confidence. The model I used is one of the simplest models, and the growth factors I used are pretty much guessed. Even so we know something for certain: it can be really bad, even if we try our best.

So yeah, you should still perform social distancing in order to help others, particularly those that are more susceptible such as the elderly; by reducing the growth factor we give breathing room to the healthcare system.

But you will get infected, or at least you should operate under that assumption, it’s only a matter of when.

To keep track of the number of cases per country in real time you can use this graph I developed. I will publish more graphs as I have them.

2 thoughts on “What does “flatten the curve” really mean?

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