Why the Impact of COVID-19 is so Difficult to Forecast

 It seems like everyone has their own opinion about the how COVID-19 will spread and impact the economy. While it is tempting to weigh in, even before COVID-19 we were skeptical of macro forecasts and predictions. We covered our views on this subject in this post, but our thoughts can more or less be summed up by the following remark from Charlie Munger:

“Projections, while they are logically required by the circumstances, on average do more harm than good.”

Interestingly, we believe that certain aspects of the spread of a virus make it particularly challenging to forecast. This is the realm of Chaos Theory, which in layman’s terms is the study of how and why some systems are difficult to predict.

We are by no means experts on this topic (and welcome experts to tell us where we are wrong). However, we recently finished Deep Simplicity by the British astrophysicist John Gribbin and were struck by its implications for understanding the pandemic. We just think it offers a really interesting mental model through which to view this problem.

In summary, the spread of COVID-19 could be interpreted as a “system” with many inputs (current people infected, contagousness, travel patterns, fatality rate, gestation, etc.) and many outputs (future people infected, deaths, economic impact, etc.). A few simple rules borrowed from Chaos Theory relating these inputs and outputs can help frame just how difficult it is to accurately predict the spread and impact of the virus.

Sensitivity to Initial Conditions

The first factor borrowed from Chaos Theory is sensitivity to initial conditions, meaning how sensitive an output is to a very small change in an input. Chaotic systems tend to be very sensitive to their initial conditions.

“What really matters is simply that some systems are very sensitive to their starting conditions, so that a tiny difference in the initial ‘push’ you give them causes a big difference in where they end up.”

In the case of COVID-19, any forecasts are very sensitive to our assumptions about the inputs mentioned above. It is very difficult to predict how many people will eventually get the disease because if we incorrectly estimate one factor, such as how many people are likely catch the virus from someone who is already infected (the R0 or basic reproduction number), we will end up with a very inaccurate prediction.

“These equations turn out to be very unstable, in the sense that a small error in one part of the calculation leads to a big error later on.”

These errors are non-linear, meaning they compound over time. So a slight error in our input estimation will have a much larger impact on our 3-month forecast than our 3-day forecast. This is the same reason that meteorologists can accurately forecast tomorrow’s weather but not next month’s weather.

“With a linear system, if I make a small mistake in measuring or estimating some initial property of the system, this will carry through my calculations and lead to a small error at the end. But with a nonlinear system, a small error at the beginning of the calculation can lead to a very large error at the end of the calculation.”

Here is what 80 days of exponential growth looks like if you change the growth factor by increments of only 0.25%. These lines could represent the cumulative amount of U.S. cases, with the blue line roughly corresponding to the actual spread of the virus.

Source: Kaho Partners

Clearly, small changes in exponential inputs can produce very large errors in estimates of future outputs.

Feedback

The second factor is feedback, which is simply that what system does affects its own behavior. A simple example of feedback in a system is a thermostat on a cold winter day. When the temperature in a room drops below a certain threshold, the thermostat turns on the heater. Once the temperature rises above another designated threshold, the thermostat turns off the heater, and the temperature begins dropping again. This process is predictable as we can know what the temperature parameters are and the feedback is instantaneous.

There is a lot of feedback going on in relation to COVID-19. The most obvious is that the more people get sick, the more healthy people take precautions. Other examples are governments shelter-in-place mandates and economic stimulus.

However, the reasons these feedback loops make predicting the spread and impact of COVID-19 even more difficult is that (1) we do not know what these parameters are in advance and (2) there is a dynamic of lead-lag between the inputs and the feedback.

We think the latter is particularly impactful here. Evidence suggests that people are typically contagious for about a week before they start to show symptoms, meaning that any feedback to the spread of the virus is likely to be based on “old” inputs.

Network Density

The third factor is network density. It turns out, the level of interconnectedness of the actors in a system has a huge impact on the likelihood that an input will cascade through the system and wreak havoc.

“What matters is the density of the network of critical points in the system.”

This is the reason that adding one grain of sand to a sandpile or one hiker’s step to a mountain of snow can cause an avalanche - the grains of sand and flakes of snow are interconnected by friction. The same phenomenon is at work with a virus - the level of interconnectedness of the world has a direct impact on the speed and magnitude of spread.

Consider how much more interconnected the world has become over the last few decades. Here is global air travel, for example:

Source: International Air Transport Association

Another scary example is watching a group of college students from a single Ft. Lauderdale beach spread across the country after “spring break” ended a few weeks ago (during the pandemic).

These ideas borrowed from Chaos Theory - sensitivity to initial conditions, feedback , and network density - illustrate just how hard it is to predict the spread and impact of a virus like COVID-19. Gribbin offers a fitting conclusion when he writes,

“In practice it is impossible to predict in detail what is going to happen more quickly than events unfold in real time.”