Exponentials And Social Distancing

Though I was quite hesitant to sit down and write this at first, I then realized that in light of the situation we are all facing right now, and what I have seen unfold earlier today in some countries like the USA, this may turn out to be useful.

Disclaimer: Before we begin, let me say upfront that I am -very- far from being a mathematical genius, an expert in crisis management nor am I claiming to be a qualified epidemiologist. I am also not in a position to lecture each country on what it ought to do to protect its citizens. I have however been in the Learning & Development space for quite some time, and that has often “influenced” me to strive to simplify complex matters for people. Though I suspect something similar may exist out there on the net, I’m hoping I can contextualize the ideas of exponentials and social distancing.

For the sake of this short article, we will assume that we are dealing with just one virus that is floating around a fictitious planet, Krypton (why not?). The virus, which we will call Krypto-19 is about to infect the first Kryptonian and operates according to the following simple principles:

  • It doubles every day, meaning that every infected individual will pass this on to 2 other people by close contact. We also assume the planet is heavily populated.
  • Once Kryptonians are infected, they become carriers for an undetermined period of time, however if they do recover they will not relapse.
  • The planet, an entirely open space, is only made up of one country where people are friendly and hug to greet each other all the time as a golden, unbroken rule, transmitted by their ancestors.
  • Lastly, we will consider no specific measures exist to prevent or slow down viral spreads like this one, and 61 days are required to develop a suitable vaccine/cure. Therefore, the virus will only be spreading around for 60 days.

How many people will the virus end up infecting in those 60 days?

If you have basic math skills (or excel), then you can figure out that the number is a little under 576.5 Quadrillion Kryptonians. In case you are having trouble with that, the number of infections on the 60th day will be precisely 576,460,752,303,423,000.

If you think that is scary, wait. There is more.

If we assume that number above represents the total infections on the planet before they get a vaccine, then on which day would only 1% of those Kryptonians have contracted the virus? I’ll wait as you multiply our astronomical number by 0.01.

As you have realized, this would occur somewhere between the 53rd and the 54th days, which means the other 99% of the total infected population caught the virus just in the last days and that is exactly the trouble with this idea of exponential growth in this situation. This is reflected in the image above this article, in which nominal increases at the beginning are barely visible in comparison to the outburst that occurs at the end of the 60 days. The reason why this is too hard for many of us to wrap our heads around this concept is simply that we are accustomed to thinking linearly, very much like how we look at a bank loan payments. The real danger is in thought processes along the lines of “it’s just 123 cases”, or “it’s only 47 more cases today” and this has already become apparent in many countries, with others to follow.

We can take this little simulation a (grim) step further: imagine Krypto-19 has a mortality rate of say, I don’t know…4 percent. I’ll let you do the numbers on that one.

Let’s get back to Earth, where a mere 7.7 billion of us we are facing an epidemic experts are calling “unprecedented in our lifetime”. Though we know very little about this COVID-19, we have proof that each person can pass the virus on to more than just 2 people every day. In short, it spreads faster that Krypto-19. It is also appearing to be lethal to those who are immunocompromised mostly.

However, in contrast to the Kryptonians, the people of the Earth can choose to consciously make a deliberate choice immediately and apply strict social distancing measures. The mortality rate of the COVID-19 coupled with the exponential contagion factor are precisely why you need to stay home, to stay away from people and to avoid contact with senior citizens at all cost.

Much like parasites, viruses require hosts to survive and therefore, collectively distancing ourselves from each other will help slow it down and neutralize its spread. At this point in time, any person could literally put other peoples’ lives at stake in a very real sense.

This incredibly poignant GIF brilliantly makes that point in a few seconds, and clearly illustrates why social distancing must be seen for what it has now become: a necessary human act of moral and social responsibility.

I hope you found this short article useful.

Please feel free to share your feedback with me and meanwhile, remember to wash your hands correctly.