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COVID-19 – A case of not grasping exponential growth

27032020_COVID-19 Compounding

COVID-19 – A case of not grasping exponential growth

Albert Einstein once said: “compound interest is the eighth wonder of the world”. The following quirky paper-folding example illustrates how compounding can hold unintuitive results, and there are a number of takeaways from this as they relate to the outbreak of COVID-19.

If you were to fold a piece of paper, how many times would you need to fold it in order for it to reach the moon? A standard piece of paper is 0.10 millimetres, and the moon on average is 384,400 kilometres away from the earth. Put another way, how many times would the 0.10 millimetre sheet of paper need to be folded in order to reach 384,400,000,000 millimetres?

Intuitively, if you were to take a quick guess, you’d have to imagine that the number of folds would be very, very large. However, as with most examples of compound interest, the result is often unexpected, given that the human brain is notoriously bad at interpreting non-linear growth patterns.

When you fold a sheet of paper its size doubles after each fold. The thickness of the paper may be small initially, but as shown by the chart below, it rises exponentially after enough folds. The sheet of paper needs to be folded only 42 times in order to be thick enough to reach the moon.

Annotation 2020-03-27 105448

The chart above is revealing, and up until the 36th fold it appears as though the paper will never reach the moon. Unfortunately, the world currently finds itself in a situation where the concept of compounding isn’t being discussed for a benign example such as folding paper, or for generating long-term wealth in the stock market. Rather it’s being applied to the COVID-19 outbreak, and the number of new cases being reported each day.

For infectious viruses such as COVID-19, a metric called R0 is used, referring to the average number of people who will catch the disease from one contagious person. Sometimes referred to as the reproduction number, R0 in other words represents how infectious the virus is. An R0 that exceeds 1 means that each existing infection will cause more than one new infection, and the virus will thus continue to spread.

According to the MRC Centre for Global Infectious Disease Analysis at Imperial College London, COVID-19 has an R0 of between 1.5 to 3.5. Ranges for R0 will vary based on a number of factors, but let’s assume in our illustration of how the virus spreads that the reproduction number is 2.

If we begin with one person who has the coronavirus, an R0 of 2 means that 2 additional people will be infected. These two new coronavirus cases will each cause two more new cases, for an incremental total of 4 new cases. The new case number then increases to 8, 16, 32, 64, 128, 256, so on and so forth. This is classic exponential growth: the growth rate remains the same (in this case the R0 and a 2x increase in the number of new cases), but the incremental case number grows larger, and larger.

The chart below looks at the global number of COVID-19 cases, and it clearly follows an exponential growth trajectory.

Annotation 2020-03-27 105623

Source: WHO via Business Insider

 As can be seen from the chart, the number of new cases is initially very small, such that the total number of infections doesn’t seem problematic. Perhaps this was why last week 20,000 Australians congregated on Bondi Beach as if there was no global pandemic: the number of cases in Australia was not yet high enough to warrant widespread alarm. Days before this spectacle, the number of coronavirus cases in Australia stood at around 600, far lower than many other nations and a tiny fraction of the circa 200,000 total global confirmed cases at this point in time.

However, the tendency of the human brain to understate exponential growth patterns highlights great risks in shrugging at this number and carrying on business as usual in Australia. Take Italy, for example. In late February they had 600 cases. Less than one month later the number of coronavirus cases in Italy has risen to over 69,000, a staggering increase in a very short period of time.

While Australia is now beginning to implement stricter measures including the closing of establishments such as restaurants and gyms, this arguably should have been done much sooner. Governments are balancing the desire to contain the virus with the hope of minimising the economic fallout. Perversely, if they had a deeper appreciation for exponential growth patterns, they would have concluded that stricter measures earlier would make the virus much easier to contain, and while painful in the short term, would also minimise the long-term economic impact. However, that’s a bitter pill to swallow, particularly if you’re a politician trying to remain in favour with a populace that also likely underestimates the implications of the non-linear growth trajectory of COVID-19.

This post was contributed by a representative of Montgomery Investment Management Pty Limited (AFSL No. 354564). The principal purpose of this post is to provide factual information and not provide financial product advice. Additionally, the information provided is not intended to provide any recommendation or opinion about any financial product. Any commentary and statements of opinion however may contain general advice only that is prepared without taking into account your personal objectives, financial circumstances or needs. Because of this, before acting on any of the information provided, you should always consider its appropriateness in light of your personal objectives, financial circumstances and needs and should consider seeking independent advice from a financial advisor if necessary before making any decisions. This post specifically excludes personal advice.


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  1. Michael Winter

    The misunderstanding can be on both sides of the equations after all it is impossible for it to stay exponential ad infinitum, i.e. once infect everyone no one else to infect, constrictions on travel of the disease, once everyone is infected in an area you can no longer infect any one else unless you move to a new area. Most epidemiologists refer to it as a bell curve rather than exponential which is more accurate and far less panic inciting. Also exponential doesn’t account for people who might be immune or resistant to it either. Just some thoughts.

  2. It helps, if we are going to talk about exponential data to display the Y-axis on an exponential scale.
    On that scale the trend should be linear if it is completely exponential.
    However, if it rises or dips then it could signify a different trend e.g. linear trends tend to flatten out whereas exponential trends will rise further

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