Herd Immunity Modeling & Coronavirus Implications

Chaos theory applies neatly to the spread of the coronavirus, in that seemingly tiny decisions or differences in reaction speed can have inordinate consequences. Effects can seem random when, in fact, they trace to discrete decisions made long prior. For example, the United States has surpassed 125,000 deaths from COVID-19. Having suppressed the virus early, South Korea has had only 289. Vietnam’s toll sits at zero. Even when differences from place to place appear random, or too dramatic to pin entirely on a failed national response, they are not.

There is enormous variation even within the U.S., which could also seem chaotic. Some places took limited measures and were barely hit; others locked down but suffered greatly. New York City has been slowly reopening since early June, but despite that—and despite mass outdoor gatherings in the throes of civil unrest over the past six weeks—the city has not seen even a small increase in daily reported cases. By contrast, other cities that have attempted to reopen have seen incapacitating surges.

But just as barely predictable meteorological events arise from totally predictable laws of physics, the complex dynamics of a pandemic center on an extremely limited set of concepts in basic viral biology. Early failures to test and shut down in the U.S. have been amplified through the butterfly effect. Current decisions will be as well.

In the absolute simplest, linear model, if 70 percent of the world were to get infected, that would mean more than 54 million deaths.

But the effects of the coronavirus are not linear. The virus affects individuals and populations in very different ways. The case-fatality rate varies drastically between adults under 40 and the elderly. This same characteristic variability of the virus—what makes it so dangerous in early stages of outbreaks—also gives a clue as to why those outbreaks could burn out earlier than initially expected. In countries with uncontained spread of the virus, such as the U.S., exactly what the herd-immunity threshold turns out to be could make a dramatic difference in how many people fall ill and die. Without a better plan, this threshold—the percentage of people who have been infected that would constitute herd immunity—seems to have become central to our fates.

Some mathematicians believe that it’s much lower than initially imagined. At least, it could be, if we choose the right future.

In a pandemic, the heterogeneity of the infectious process also makes forecasting difficult. When you flip a coin, the outcome is not affected by the flips prior. But in dynamic systems, the outcomes are more like those in chess: The next play is influenced by the previous one. Differences in outcome can grow exponentially, reinforcing one another until the situation becomes, through a series of individually predictable moves, radically different from other possible scenarios. You have some chance of being able to predict the first move in a game of chess, but good luck predicting the last.

“We just keep running the models, and it keeps coming back at less than 20 percent,” Gomes said. “It’s very striking.”

If that proves correct, it would be life-altering news. It wouldn’t mean that the virus is gone. But by Gomes’s estimates, if roughly one out of every five people in a given population is immune to the virus, that seems to be enough to slow its spread to a level where each infectious person is infecting an average of less than one other person. The number of infections would steadily decline. That’s the classic definition of herd immunity. It would mean, for instance, that at 25 percent antibody prevalence, New York City could continue its careful reopening without fear of another major surge in cases.

It doesn’t make intuitive sense, Gomes admits, but “the homogenous models just don’t make curves that match the current data,” she said. Dynamic systems develop in complex and unpredictable ways, and she believes that the best we can do is continually update models based on what is happening in the real world. She can’t say why the threshold in her models is consistently at or below 20 percent, but it is. “If heterogeneity isn’t the cause,” she said, “then I’d like for someone to explain what is.”

By definition, dynamic systems don’t deal in static numbers. Any such herd-immunity threshold is context-dependent and constantly shifting. It will change over time and space. It varies depending on the basic reproduction number—the average number of new infections caused by an infected individual. During the early stage of an outbreak of a new virus (to which no one has immunity), that number will be higher. The number is skewed by super-spreading events, such as when one person in a choir infects 50 others. And the number in a dense city such as New York should be expected to be higher than that in rural Alaska. “Within certain populations that lack heterogeneity, like within a nursing home or school, you may even see the herd-immunity threshold be above 70 percent,” Bansal says. If a population average led people in those settings to get complacent, there could be needless death.
For all the mysteries of how this virus affects our bodies and immune systems, and all the heterogeneity involved in the complex modeling of outcomes, Bansal believes that heterogeneity of behavior is the key determinant of our futures. “That magic number that we’re describing as a herd-immunity threshold very much depends on how individuals behave,” Bansal says, since R0 clearly changes with behaviors. On average, the R0 of the coronavirus currently seems to be between 2 and 3, according to Lipsitch. But if we all sealed ourselves in isolation pods today, the R0 would drop to zero. There would be no more deaths.

“COVID-19 is the first disease in modern times where the whole world has changed their behavior and disease spread has been reduced,” Britton noted. That made old models and numbers obsolete. Social distancing and other reactive measures changed the R0 value, and they will continue to do so. The virus has certain immutable properties, but there is nothing immutable about how many infections it causes in the real world.

What we seem to need is a better understanding of herd immunity in this novel context. The threshold can change based on how a virus spreads. The spread keeps on changing based on how we react to it at every stage, and the effects compound. Small preventive measures have big downstream effects. In other words, the herd in question determines its immunity. There is no mystery in how to drop the R0 to below 1 and reach an effective herd immunity: masks, social distancing, hand-washing, and everything everyone is tired of hearing about. It is already being done.

“I think it no longer seems impossible that Switzerland or Germany could remain near where they are in terms of cases, meaning not very much larger outbreaks, until there’s a vaccine,” he said. They seem to have the will and systems in place to keep their economies closed enough to maintain their current equilibrium.

Other wealthy countries could hypothetically create societies that are effectively immune to further surges, where the effective herd-immunity threshold is low. Even in the U.S., it’s not too late to create a world in which you are not likely to get the coronavirus. We can wear masks and enable people to stay housed and fed without taking up dangerous work. But, judging by the decisions U.S. leaders have made so far, it seems that few places in the country will choose to live this way. Many cities and states will push backwards into an old way of life, where the herd-immunity threshold is high. Dangerous decisions will be amplified by the dynamic systems of society. People will travel and seed outbreaks in places that have worked tirelessly to contain the virus. In some cases, a single infected person will indirectly lead to hundreds or thousands of deaths.

We have the wealth in this country to care for people, and to set the herd-immunity threshold where we choose. Parts of the world are illuminating a third way forward, something in between total lockdown and simply resuming the old ways of life. It happens through individual choices and collective actions, reimagining new ways of living, and having the state support and leadership to make those ways possible. For as much attention as we give to the virus, and to drugs and our immune systems, the variable in the system is us. There will only be as much chaos as we allow.