The Non-intuitive Math of Pandemic Risk
At the time of this writing, COVID-19 has brought the world to a standstill. In the US and most other countries, citizens are on lockdown and economies are essentially on pause in an effort to slow the virus’ outbreak.
Many are struggling to understand why this particular virus has provoked such a drastic and unprecedented response. That confusion is a good example of how our mind interprets data and calculates risk.
Some key heuristics and biases are at play:
Framing. We evaluate information based on simple comparisons, not rational calculations. Different comparisons can make the same information look drastically different (I wrote about framing and COVID-19 in a recent newsletter).
Anchoring. Those comparisons are often completely arbitrary, and whichever one comes to mind first is weighed disproportionately.
Availability bias. Our anchors and comparisons are often just whatever comes to mind the easiest.
Exponential growth bias. We assume growth is linear, rather than exponential, and significantly underestimate the power of compound growth.
Let’s walk through how these can affect our impression of the virus’ severity and how infectious disease experts view it differently.
The most common anchor is the flu. Looking at raw numbers, the flu appears much more deadly, as it kills 30,000 to 60,000 Americans every year. Meanwhile, COVID-19 has only resulted in only 7,426 deaths worldwide to date (source: Our World in Data). With this framing, it feels like we’re overreacting.
Availability bias may bring on comparisons to other deadly problems like heart disease or car crashes, which cause 647,000 and 1.25 million deaths in the US each year. Again, it feels like there are far more serious issues to deal with than this.
Epidemiologists and other experts in infectious diseases are primarily anchored to other, less intuitive metrics.
One is growth rate: how quickly is the disease spreading? The mathematical term for a virus’ growth rate is R0 (pronounced “R naught”), which indicates how contagious it is. Basically, it tells the average number of people who will catch a disease from one contagious person. A disease with an R0 greater than 1 will naturally grow, as each case will create more infections.
Let’s use an example to understand this. In 2019, Amazon generated $280.52B in revenue according to Statista. Walmart, considered its biggest competitor, generated significantly more: $514.41B.
However, Amazon is much, much more valuable according to investors. Its current market capitalization is $904.45B according to YCharts, while Walmart’s is merely $353.43B.
Why is Amazon worth so much more than Walmart despite significantly less annual revenue? Investors believe Amazon is, and will continue to, grow much faster. Investment value is based on the future, not the present.
Similarly, experts believe COVID-19 is growing, and will continue to grow, at a much faster rate than other ailments unless drastic measures are taken. Estimates for COVID-19’s R0 seem to range from 2 to 2.5, meaning that each person with the virus will, on average, spread it to at least 2 additional people. The flu, by comparison, has an R0 of 1.3, meaning that it does grow, but slowly. It also has a vaccine, ensuring many people can never get it in the first place, and known medical treatments for the infected. COVID-19 has neither yet, so containing that growth with traditional medical means is a challenge for now. We can now also understand why comparisons to dangers like heart disease or car crashes are unhelpful. Neither are contagious and have the ability to grow on their own.
So, what exactly does that growth rate mean? The math is not intuitive - this is where exponential growth bias kicks in. For example, imagine you have a dollar that doubles in value every day. How much money will you have after a month?
After just 31 days, you’d have more than $1 billion.
Our minds assume growth is linear, but something that can double itself grows exponentially. It takes on a hockey stick shape as in the chart below, not a straight line.
Why does that growth matter? Data currently shows 80% of cases are “mild” or “moderate” and do not require medical assistance, so while a lot of people would get sick, it doesn’t appear catastrophic.
Two more important metrics factor into the experts’ concerns: hospitalization and fatality rates.
According to the American Hospital Association, around 20% of cases require medical care, 5% are hospitalized, and 1% need the support of ventilators. The number of medical professionals, hospital beds, and ventilators are relatively fixed - we can’t train more doctors or manufacture more ventilators very quickly. So, if the growth rate continues unabated, the demand for those resources will quickly exceed the supply.
The final key data point, fatality rate, seems to be heavily impacted by that medical capacity so far. Once that saturation point hits, the fatality rate seems to increase significantly:
…countries that are prepared will see a fatality rate of ~0.5% (South Korea) to 0.9% (rest of China [outside of Wuhan]).
Countries that are overwhelmed will have a fatality rate between ~3%-5%.
There appears to be an alarming difference in deaths between areas that are unable to slow the spread and overwhelm their medical system - like Wuhan and Italy - and those that are able to keep the spread on pace with the necessary resources - like South Korea, Singapore, and the rest of China that had more time to react.
The fatality rate may seem hard to comprehend, too. 3% doesn’t sound like that much on its own. After all, 97% of people end up being okay in that case.
Change the framing by applying that number to big enough populations, though, and the numbers get scary. The most advanced forecasting models on the virus so far have been done by researchers at Imperial College London. Their research has reportedly been driving the decision-making of government leaders in both the US and UK. They estimated that, without taking precaution to slow down the spread, 81% of US and UK residents would become infected (assuming an R0 of 2.4). As a result, 2.2 million would die in the US and 510,000 would in the UK (source).
Now, of course, we are taking measures to slow down the spread, and will continue to, so such a nightmare scenario is very, very unlikely. The point is that this is what can happen with a virus that spreads so quickly.
These calculations are not intuitive, but they are what the world’s leaders are basing their decisions on.
The more relevant debate is how we should respond to that risk. The best data we have show that the virus is likely to grow more quickly than our ability to properly treat it, so slowing that growth as much as possible buys us time. However, there are real costs to containment procedures and they can’t be done forever.
For now, the US and most other countries have taken extreme precaution to avoid worst-case scenarios. In a future post, I’ll write about decision-making under such risk and uncertainty.