Protests erupting across the nation over the past week — and law enforcement’s response to them — are threatening to upend efforts by health officials to track and contain the spread of coronavirus just as those efforts were finally getting underway. Health experts need newly infected people to remember and recount everyone they’ve interacted with over several days in order to alert others who may have been exposed, and prevent them from spreading the disease further. But that process, known as contact tracing, relies on people knowing who they’ve been in contact with — a daunting task if they’ve been to a mass gathering. And the process relies on something that may suddenly be in especially short supply: Trust in government. “These events that are happening now are further threats to the trust we need,” said Dr. Sandro Galea, dean of the Boston University School of Public Health. “If we do not have that, I worry our capacity to control new outbreaks becomes more limited,” he said. Government officials have been hoping to continue reopening businesses, churches and other organizations after months of stay-at-home orders and other infection-prevention measures. But health experts also hoped that any reopening would be accompanied by widespread testing, contact tracing and isolation to prevent new waves of illness from beginning. Over the past week, protests sparked by the death of George Floyd, a black man who died after a white Minneapolis police officer pinned a knee to his neck, have involved thousands of people gathered tightly together in large crowds in more than 20 cities nationwide. It’s unclear if the protests themselves will trigger large new outbreaks. The protests were outside, where infections don’t spread as readily as indoors. Also, many of the protesters were wearing masks, and much of the contact was likely less-hazardous “transient” moments of people moving around, passing each other, said Dr. William Schaffner, an infectious diseases expert at Vanderbilt University. But, still, experts worry that public efforts to contain the disease in the future could be undermined.