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Understanding exponential growth to prevent pandemics

The recent COVID-19 global pandemic revealed that most people underestimate exponential growth, especially when it comes to speed of the spread of the disease.
While COVID-19 made us familiar with terms such as doubling time, logarithmic scales, R factor, and exponential growth among others, the familiarity with these terms did not mean we fully comprehended the speed of the spread of the virus.

Exponential growth is in particular a notoriously difficult concept to understand. There is this old Indian legend about a king who wanted to reward one of his advisers. Asked what he wanted, the adviser said he would be happy with a grain of rice placed on the first square of a chessboard, and to double the amount of grains for each of the 63 subsequent squares on the board.

Unaware of the exponential growth involved, the king agreed, only to find that by doubling the amount of grain for each of 64 chessboard squares, he would end up providing the advisor with 18 quintillion, 446 quadrillion, 744 trillion, 73 billion, 709 million, 551 thousand and 615 grains. To put this number in more perspective, to ferry all that rice grains would involve more than 11 billion train carriages filled to the brim. In more picturesque language, the 11 billion train carriages, if placed bumper to bumper, would go around the world at the equator 6,325 times.

Obviously, the ability to grasp the magnitude of exponential growth depends on the way in which it is communicated. Using the right framing helps to understand the huge numbers involved when it comes to global pandemics, or in implementing mitigation measures. Underestimating exponential growth often results in negative consequences during a pandemic, with people misjudging how quickly the virus can spread, and therefore delaying mitigating measures such as wearing masks, social distancing, or staying at home during an outbreak.

This behavioral phenomenon, known as ‘exponential bias’ is the subject of a new research paper published by researchers at ETH Zurich’s Center for Law and Economics and the Lucerne University of Applied Sciences and Arts in Switzerland. They wanted to find out whether the way in which the exponential spread of infectious disease is communicated can affect the magnitude of this bias.
Most people when they talk of growth are intuitively inclined towards linear growth, which is for example ( 3-6-9-12-15…). This leads them to vastly underestimate the speed of exponential growth (3-9-27-81-243…). From previous experiments, the researchers knew that people underestimate exponential growth even when they are aware of exponential growth bias. In other words, informed people still underestimate what exponential growth really means in practice.

For their study, the researchers presented 400 participants with the same scenario: a country currently has a thousand cases of viral infection, and this figure climbs by 26 percent every day. With this exponential spread of the virus, the country would reach one million cases in 30 days. However, there is a chance to reduce the growth rate from 26 percent to 9 percent by adopting mitigation measures.

Researchers quizzed participants on the situation, framing their questions from different perspectives: How many cases can be prevented by adopting mitigation measures? By adopting the measures, how much time can be gained before reaching one million cases? How many cases will there be after 30 days if mitigation measures lengthen the doubling time from three days to eight days? By the way, extending the doubling time like this is equivalent to reducing the growth rate from 26 percent to 9 percent — something that few people recognise intuitively.

The first finding from the study was that talking about growth rates is an ineffective way of communicating the spread of pandemic diseases. Over 90 percent of participants drastically underestimated the number of infections after 30 days of exponential spread. They were much more on the mark, however, when the question was framed using doubling times.

The second finding was that people have trouble gauging how many infections can be prevented with mitigation measures. When asked how many infections could be prevented in the scenario above (starting from a thousand cases, a growth rate of 9 percent instead of 26 percent over 30 days), people responded with estimates that were extremely far off. The typical (median) participant believed that 8,600 cases could be prevented, when, in fact, the figure is almost one million.

However, when participants were asked about the number of days that could be gained by adopting mitigation measures — for example, until hospitals are overloaded, or until there is a vaccine on the market — their estimates were significantly better. The experiment achieved its best results when questions were framed from the perspective of time gained and the impact of slowing down doubling times.

A statement that combines both of these would be, for example: “If each of us adopt preventative measures today, cases of the virus will slow down — we can estimate that they will double only every eight days, as opposed to every three days. This allows 50 additional days to implement preparatory measures to combat the virus (e.g., by providing much needed supplies to hospitals, or finding treatments and vaccines) before reaching one million cases.”

The research team added that pandemic measures are just one application of the framing theory when it comes to communicating exponential growth: similar phenomena might also be observed in the banking and finance industry, or when it comes to legal or environmental policy-making, especially with regard to disseminating information on climate change and greenhouse gas emissions.



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