She noted, however, that game theory assumes people are rational in their decision-making. Fear can suppress vaccination “to precarious levels insufficient to prevent the spread of an outbreak,” she said.

A 2019 investigation using game theory to study vaccination showed that vaccine hesitancy could be explained by a mathy mechanism called “hysteresis.” In general terms, hysteresis occurs when the effects of a force persist even after the force is removed — the response lags. Paper clips exposed to a magnetic field still cling together after the field is turned off; unemployment rates can remain high even in a recovery economy.

Similarly, even after a vaccine is deemed safe and efficacious, uptake rates often remain low.

“The hysteresis effect makes the population hysterical, or sensitive, to the perceived risks of the vaccine,” said Xingru Chen, a doctoral student in mathematics at Dartmouth College, and the paper’s co-author, with her adviser Feng Fu, a mathematician and biomedical data scientist (who recently applied a similar approach to the dilemma of social distancing).

“It boils down to a fundamental problem known as the tragedy of the commons,” Ms. Chen said. “There is a misalignment of individual interests and societal interests.” To overcome the hysteresis effect, she said, vaccination should be promoted as an act of altruism — one’s personal contribution to defeating the pandemic.

A subsequent iteration of the coronavirus game-theory study explored how vaccine compliance affects the number of deaths prevented. If a small subset of the population chooses not to get the vaccine, it affects us all, said Dr. Anand, who is also an author and a poet. Her book “A New Index for Predicting Catastrophes” includes found poems composed of words from her scientific papers.

(One poem, “The Strategy of the Majority, ” was drawn from her first paper on human-environment systems, which inspired the current study. The last line: “the price of finding equilibria is increasing.”)

Sebastian Funk, an infectious disease epidemiologist at the London School of Hygiene and Tropical Medicine, said that the coronavirus study nicely highlighted the importance of assessing how interventions aiming to contain spread during an outbreak can affect human behavior. “Excluding this from models of infectious disease transmission can be a major limitation,” he said.