# Flattening the curve?

## The statement that we encounter everywhere after the spread of the COVID-19 virus is wrong in my opinion. Why?

Posted by Fares on April 11, 2020, 8:50 p.m. Edited on July 2, 2020, 3:50 p.m.

By now you might have already heard of the new statement everywhere: « Flattening the curve ». This sentence related to the newly discovered virus COVID-19 has emerged and spread all around the globe and became a metaphor instead of saying « stay at home and avoid social contact » or « social distancing ».

But in my opinion, this sentence -or at least the meaning behind it- is wrong. Why?

Figure. 1 – A typical Flattening the curve picture that we see everywhere.

Well, to start of with, we need to understand what people (or experts) mean by flattening the curve. Basically Figure.1 shows what the picture that everyone of us has seen on the internet. The horizontal axis represents the days since the first day of the pandemic and the vertical axis represents the number of cases (or deaths). The curve in grey represents what would happen if no security measure again the virus spread are taken where we observe a peak after few days of the spread due to the exponential growth of the number of cases.

Now let’s go back to the topic, Flattening the curve which is in this case represented by the green curve in Figure.1 means to lower the maximum number of cases but increase significantly the number of days in which the pandemic is active. This can be achieve for example by social distancing or staying at home. But here comes the problem: Statistically speaking, the areas under curve in this case represents the total number of cases (infections or deaths). Flattening the curve with the previous assumptions means finding a way to lower the maximum number of cases per day. If we consider the curve as a gaussian (which is what everyone is assuming), the mean represents the day where the maximum number of cases occurs and the standard deviation represent how narrow or spread the curve is. In order to achieve such flattening (shown in), we have to shift the mean toward the right (meaning that we reach the maximum later) and increase the standard deviation (meaning that the pandemic will last longer). However, all this is based on a major starting point: both curves have the same area, which means the number of cases should be the same and we will just gain time.

This is however a wrong assumption. If we take some serious measures, such as social distancing the number of cases at the end of the story is not going to be the same because fewer people will get infected because the virus finally disappears (or theoretically speaking a vaccine is found). Thus, with social distancing for example, the area is not the same and the figure is no more valid.

Figure.2 – How should the real curve look like.

So how does the actual « Flattening the curve » figure look like Fares? Well if we take into consideration all previous facts and conclusions i.e., reduce the maximum and having a smaller area (less infections) we should get the curve shown in Figure.2. What this tells us is that if our defence strategy is well designed, the peak should take place in the sane day and the pandemic should last for the same number of days. The only thing that should change is the areas (number of total infections).

Figure.4 – The curve in a real world scenario.

Of course the discussion above is for a perfect scenario in which everything should work as a binary. In the real world, people man not respect the law, governments may take late decisions and many more factors that can affect the real curve (such as the authenticity of the number of cases etc.). And hence, the real practical curve might look something like what is shown in Figure.3. The day where the peaks happens shifts toward the right (similar to Figure.1) but still, the surface under the curve should be smaller.

At the end, I want to say that this was only my opinion based on personal analysis. If you have some comments, please let me know. Thank you for reading.