Downside up, upside down: Tracking COVID-19 along the S-curve

A few years ago I shared lessons from work I did between 2006 and 2012 in China helping McKinsey and our clients build reliable models for the evolution of consumer demand. Over the past few weeks, I have seen how these lessons can be relevant for understanding data on the spread of the COVID-19.

To be clear, I am no medical scientist, but I do have experience analyzing data. Here I’d like to broadly apply lessons we learned from working on various demand models to some of the available data on the virus.

For a more comprehensive briefing on the wider implications of the virus on business, I strongly recommend you read this excellent article on McKinsey.com

Recognize the S-curve

There is a famous line in Ernest Hemingway’s novel The Sun Also Rises which is similarly applauded by English professors, technologists, bankers, and epidemiologists. The character Mike Campbell is asked how he went bankrupt and replies, “Two ways. Gradually and then suddenly.”

Campbell’s answer succinctly captures the nature of most phase transitions. These changes happen all around us and yet we don’t fully intuit them. Sunrise, earthquakes, the freezing of liquid, the life cycle of a butterfly, getting a promotion, joining the army, bankruptcy and yes, even viral pandemics are just a few of the many examples of transitions in nature and life. The thing is, these changes feel sudden and capricious, but they are all preceded by a gradual and often predictable progression. 

Most phase transitions follow an S-curve. At first, the transition happens slowly, then rapidly and then slowly again. If you’ve ever made popcorn you’ve experienced this first hand. You apply heat to the corn and at first, the pops come slowly before speeding up and then slowing back down again. Now you know it’s ready (or about to burn).  

Zoom into an S-curve, though, and this progression seems linear. Linear change feels more intuitive, but few phenomena are ever linear for long. The idiom ‘spreads like wildfire’ describes the sharp increase of an S-curve. It’s not only sudden, but it also seems uncontrollable. If it’s bad, like COVID-19, it quickly becomes ‘scary bad’. If it’s good, like for instance growth in demand for a product, it quickly feels euphoric. But in both cases, the current state of affairs will not last forever and is almost often shorter than we fear or hope.

So, if the first lesson is to recognize the s-curve, the next and more important one is to anticipate its evolution and try to avoid complacency or panic.

Find the upward inflection point

When we were modeling the evolution of consumer demand for businesses in China, we foresaw (though in some cases still under-estimated) growth acceleration in many categories. This prediction was based on the knowledge that linear income growth eventually translates to exponential growth in discretionary spending. Just like that popping corn, income gradually heats up and grows. At first, it’s still not enough to buy a car, and then suddenly with a pop, it is.

In each category, we carefully studied these inflection points, not only nationally but in every province and city, and then we used data to direct resources and capture demand wherever it was about to pop.

Search for the slowdown

It’s a little harder to determine when this accelerated phase will end. Although it is relatively easy to understand its limits. Demand curves will always slow down when penetration matures (though they may slow sooner and even suddenly, for example with what we know as product fads). Fires naturally slow down when they have nothing left to burn or other forces intervene.

It’s also interesting to consider the simple mathematical law benchmark that Neil Johnson, a physicist, discovered studying the distribution of various dynamic network models. He mapped the distribution of event clusters by their severity or size across many unrelated and seemingly random domains such terror, cyber-attacks, war causalities, protests against the government, earthquakes, or transaction size by traders in the same stock exchange. He’s shown they all follow a curve with an approximate slope of 2.5. The occurrence of events with higher severity is exponentially rarer with this slope (or power-law exponent).

Knowing little about a given virus, and despite many random variables on how it may spread, this allows us to simplify and normalize a prediction model. Together with others, he did create models that could predict the duration and severity of virus contagion (e.g. Zika in 2016) based on the flow of people through popular places such as airports and schools. Another fascinating mathematical application of his work is on understanding the resilient dynamics of online hate and estimating the effect of different intervention policies.  

With all that let me make a few observations about predicting the shape of the current pandemic s-curve.

Let me be crystal clear–this is simply an analysis of how to read and interpret numbers. I am not qualified to make any medical judgment.

1.    Comparing countries can be helpful to understand early inflection points  

When consumer companies want to understand the relationship between income and demand for a product category they often look at development in other countries. There can be reasons why the same will not apply–for example, differences in culture, weather, and infrastructure–but with some adjustment, a country to country comparison is probably helpful. This chart comparing Italy and the US bears out this principle. 

2.    Comparing countries to figure out when infection growth will slow down can be misleading without fully understanding the differences in response

The virus is infecting people in similar ways, but the response to that infection has been very different between countries as the next chart illustrates when you compare what happened in Guandong, Zhejiang, and Taiwan who took strong already actions on 24th of January versus Italy on March 4th (12 days later in terms of when the spread started to grow fast).

3.    Beware of comparing apples to oranges.

Data is rarely ready for analysis without a significant amount of cleaning to make it fully comparable. This is definitely the case with the data on COVID-19 where we see any number of instances where we are in danger of comparing apples to oranges.

One prominent example is in the huge variability in the amount of testing between countries. This variability makes it especially hard to compare death rates. As health care systems become busier it’s likely they will test fewer patients with mild symptoms. Likewise, some concentrated testing efforts may make a specific day look like a scary jump. Finally, reporting standards may differ from place to place. It’s important to be aware of this

In conclusion

On the upside, given the data we have, it’s reasonable to make an accurate prediction about the upward inflection point of the virus: even when the numbers of people infected are small they are likely to double every 2-4 days without a major response from the government.

On the downside, while we can predict the limits of the pandemic, it’s close to impossible to predict when the virus will start to slow down before an escalated intervention from governments.

The good news is that we know this pandemic will come to an end. And as we’ve seen in places like Taiwan that have applied the lessons from SARS, when we work together and respond effectively, calmly, and carefully, we can contain both the fear of the virus and the virus itself.