Now the vaccine adds one more protective layer. The perceived benefits and costs of vaccination are often expressed as concerns about safety and side effects. If you are on the fence about vaccination, you might decide — noticing lower infection rates as vaccination campaigns gain speed — that it no longer seems so critical to get the jab.

“Some people might play a ‘wait-and-see game,’” Dr. Bauch said. People who choose not to be vaccinated effectively get a free ride, reaping the benefits of reduced virus transmission generated by the people who do opt for vaccination. But the free rides generate a collective threat.

“That is the prisoner’s dilemma,” Dr. Bauch said. When infection levels are low, people feel less at risk, let down their guard, and then infection levels again rise; the ebb and flow between our behavior and the virus causes the pandemic waves. “We end up in this unhappy medium,” he said.