With its small population and isolated location, Iceland has earned praise and headlines for its plan to test as many people as possible for exposure to the new coronavirus. Why, some wondered, couldn’t other countries be like Iceland?

But critics inside the country have called this rosy picture misleading.

They say the tiny Nordic island country of 360,000 people has not done enough to suppress new cases of Covid-19, the disease caused by the virus. Primary schools and day-care centers remain open, as do some restaurants with limited seating. Tourists are still allowed to arrive and travel without quarantine. The authorities at first limited gatherings to 100 people, then changed that to 20, long after other countries were imposing greater social isolation.

Iceland’s goal of testing everyone faces the same logistical hurdles that all countries face, the critics point out. It does not have enough medical personnel, supplies or hours in the day to test hundreds of thousands of people in a few weeks or months. They have warned of false optimism that will ultimately lead to more infections and death.