For the moment Rhode Island, the nation’s smallest state, walks an uncertain path. The mayors of its densely packed and polyglot cities speak of rising rates of infection. Last week, health officials announced that workers at Taylor Farms New England, which packs salads and produce for supermarkets in North Kingstown, had tested positive for the virus. By Sunday, 133 cases had been reported in connection with the facility.

Statewide, hospitalizations appear to have peaked a week ago at 277, and have dropped slightly.

Deaths from the virus reached a daily peak of 19 in Rhode Island earlier this month, according to a New York Times tally, and fell to as low as five on one day last week. By Monday, 7,708 people in Rhode Island were reported to have tested positive for the virus and 233 people had died.

In its accomplishments and struggles, Rhode Island represents much that is confounding about confronting this virus. Like most of the governors in the Northeast, Ms. Raimondo was reluctant to issue a shelter-in-place order in mid-March, hoping that social distancing and the careful tracking of routes of infection might forestall a crushing shutdown of the economy.