What do COVID-19, climate change, feuds and explosions have in common?

By March 14, 2020, there had been 47 confirmed deaths from COVID-19 across the U.S. Two days later: 68 deaths. Then 108, 150, 340, 590, 1050, 1707, 2509, 4079, 6053, 8501, 10989... The number of deaths doubled every few days. Such behavior feels alarming, out of control, inexplicable.

But, in fact, such exponential growth is characteristic of a class of phenomena well-known to science: a "reinforcing feedback loop." "Feedback loop" refers to a situation where some phenomenon, let's call it "A," influences another phenomenon, let's call it "B," and then B in turn cycles back and influences A. It's called "reinforcing" because the loop reinforces the phenomenon in question, causing it to become larger or stronger with each passage around the loop. A familiar example is a feud, in which person A does a small harm to person B, who then retaliates by harming person A, who then gets even angrier and harms person B again even worse, and so on around a vicious cycle of escalating harm.

In the case of a pandemic, we can diagram the reinforcing feedback loop as follows:

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STELLA systems diagram of COVID-19 as a feedback loop

Provenance: Kim Kastens, Lamont-Doherty Earth Observatory
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.

Each box on the diagram represents a group of people. Individuals flow across the diagram from left to right. Of the group of people who might be susceptible to the virus, some individuals become exposed. Some of those exposed become sick and thus infectious, and then sick individuals either recover or die. The valve symbols depict points at which the rate of one of these flows can be influenced.

The key to the out-of-control growth of a pandemic lies in the red influence arrow arcing back upstream, from the Sick/infectious group to the becoming exposed valve. This arrow signifies that for any given time and place, the number of people who are already infectious controls the number who become exposed. At a time and place with few Infectious individuals, the flow from Susceptible to Exposed will remain low. But as the Infectious group grows, it accelerates the growth of the Exposed group. This is the diabolical nature of a runaway feedback loop: as things get worse, they get even worse, and the worsening multiplies exponentially.

Reinforcing feedback loops are common in both natural and human-built systems. Although they look different on the surface, all share the attribute that a tiny initiator has the potential to grow exponentially into a huge effect. Chemical and nuclear explosions are reinforcing feedback loops. Addiction is a reinforcing feedback loop in which consuming a small amount of the problematic substance leads to a desire for even more. Global climate change involves multiple reinforcing feedback loops. When warming air temperature causes sea ice in the Arctic to melt, more of the incoming solar radiation warms the Arctic water, leading to yet more sea ice melting. In each of these situations, more leads to even more. Infected people lead to even more people becoming infected. Fissioned atoms release neutrons that trigger even more atoms to fission. Substance consumed leads to even more desire to consume. Ice melting leads to more solar energy absorption which leads to even more ice melting.

Once released, it is hard to rein in a reinforcing feedback loop. But nothing can keep growing forever. Some reinforcing feedback loops stop when they run low on input material, be that TNT, or sea ice, or susceptible individuals. The Hatfield-McCoy feud ran out of steam when a critical mass of Hatfields had been imprisoned and/or hanged. Historic pandemics ended when the pool of susceptible individuals shrank sufficiently. Feedback loops can also be disrupted by breaking or weakening a link in the loop. In a pandemic, social distancing diminishes the flow from Susceptible Individuals into Exposed Individuals, partially closing the "Becoming exposed" valve on the diagram. A COVID-19 vaccine would be a strong intervention because it would disrupt the central "becoming sick" link of the feedback loop.

Not only are feedback loops hard to control, they are hard to think about. From our own teaching and research, we know that the human mind does not cope comfortably with feedback loops. We hypothesize that this is because humans have learned, from a lifetime of experience, that time advances in one direction, from the past, through the present, to the future. Moreover, causality is tightly coupled to time: if A happens before B, then A can have caused or influenced B--but not vice versa. Asking the human mind to reason about a causal chain that loops around and bites its own tail is a cognitive challenge. When the future is determined by a reinforcing loop, it is hard to anticipate or influence the accelerating changes. The first step is to recognize the distinctive, exponential, out-of-control, pandemic-like behavior. This is an indicator that you may be in the presence of a reinforcing feedback loop, and that the most impactful interventions will require breaking or weakening a link in the loop.

Sources and references

• Numbers in the first paragraph come from Our World in Data, who obtained them from the European Center for Disease Control and Prevention. They are the total number of confirmed of deaths in the United States from March 14 through April 8, 2020, every 2^ndday.
• MetaSD provides a video description of a more elaborate model of COVID-19 spread as a reinforcing feedback loop, based on data from Bozeman, Montana. This same site includes a link to the model itself, which runs in Vensim. Both video and model are by Tom Fiddeman of Ventanna Systems.