On December 29 last year, Hasan Gokal, the medical director of the COVID-19 response team in Harris County, Texas (which includes Houston, the fourth-largest city in the United States by population), was supervising the administration of the Moderna vaccine, mostly to emergency workers. The vaccine comes in vials containing 11 doses. A vial, once opened, expires in six hours and unused vaccines must then be thrown away.

On that December day, a patient arrived just before closing time, so a nurse had to open a new vial, leaving Gokal with 10 doses. He offered them to the health-care workers and to two police officers still on the site, but they had either been vaccinated, or declined. He called a colleague whose parents and in-laws were eligible — anyone over 65 or with a medical condition that increases the risk from the coronavirus could then be vaccinated — but they weren’t available.

Gokal started calling people from his phone’s contacts to ask if they knew anyone eligible who wanted to be vaccinated and could come to his home that evening. When he arrived home, two people were waiting there, and he vaccinated them. Then he drove to homes where he knew there were eligible people, and vaccinated five more.