Hysteresis and the Post-Reopening Coronavirus Fatality Rate

By John Banks

“Hysteresis” is a vital concept in mechanical engineering. It also applies to economics, medicine, and financial markets.

Hysteresis occurs when changes to a system happen with a time lag. It can also be defined as systemic state-dependence, meaning, whatever happens next is influenced by the past.

There is no hysteresis in, say, rolling a pair of dice. The outcome of the dice roll has no relationship with past rolls.

There can be a frustrating amount of hysteresis, on the other hand, in trying to adjust the water temperature of the shower in a house with old plumbing.

When the shower knob is turned toward “hot,” it can take time for hot water to travel to the shower head.

This creates temptation to turn the knob too far — and then to yelp when the water turns scalding hot. At this point, the normal move is to overreact in the other direction, turning the knob too far toward cold. The time lag between action and results creates confusion.

Another example of hysteresis is drinking at a party. The impact of a drink depends on how many drinks came before it, and whether they were consumed quickly or spaced far apart.

In economics and financial markets, policy actions can also demonstrate hysteresis. As with the shower in a house with old plumbing, there is often a time lag between policy execution (like turning the knob) and real-world economic impact (feeling the temperature change).

Hysteresis presents a challenge when the time lag causes confusion. It is easy to get confused by cause and effect, or to miss a cause-and-effect relationship, if the cause and the effect are spaced far apart due to a time lag. 

Take coronavirus fatality rates, for example.

One piece of good news in the pandemic, not much talked about, is how U.S. fatality rates have notably declined from previously high levels. You can see this in the chart below, via Covidcharts.com.

What was the cause of this notable decline?

As with most things related to the coronavirus, that isn’t easy to say. There are multiple factors involved, including the surge of New York City cases and deaths.

But if we apply hysteresis, we can generate a reasonable hypothesis: The decline in death rates was a health dividend earned by sheltering in place.

We know California was one of the earliest states to mandate a shelter-in-place order. That happened on March 19. Dozens of states followed suit in the two weeks that followed.

We can also see, via the chart, that the new deaths per day moving average peaked on April 21. That was roughly four weeks after shelter-in-place orders were rolled out across the country.

This makes sense because four to six weeks, as a rough average, is about how long it takes a coronavirus fatality to occur.

We can observe it takes about a week to show symptoms; perhaps another week to be hospitalized; and then an additional two to four weeks to succumb to the virus, with a final multi-day lag before the fatality is entered into public health records.

With hysteresis in mind, we can then see how sheltering in place lowered the fatality rate with a lag. The lives saved in lockdown were not apparent immediately — but they showed up as an absence in the fatality statistics four to six weeks later.

Now, here is the grim part of this analysis.

If the hypothesis is correct that sheltering in place reduced the COVD-19 fatality rate — and fatalities show up on a four-to-six week lag — we can further note that shelter-in-place directives largely ended on Memorial Day, May 25. That was also the day a rolling wave of multi-week nationwide protests began.

Based on the concept of a time lag — knowing it takes four to six weeks for fatality rates to show up in public health records — we can then hypothesize the shelter-in-place dividend is about to end.

This means that, circa end-of-June into early July — the four-to-six week window following the reopening — fatality rates are likely to start rising again.

We also know that, as of this writing, states like Florida and South Carolina have broken single-day new-case records for multiple days in a row, even as hospital systems in Arizona and Texas face severe strain, and Johns Hopkins data indicates rising average caseloads in 29 states.

The critical test here will be what happens to the new deaths per day statistic — which is trackable via Covidcharts.com — over the next few weeks.

If we see a meaningful upturn in the new deaths per day moving average between now and Independence Day, watch out.