The coronavirus has infected far more people in the United States than testing has shown so far, and stringent measures to limit social contact in parts of the country not yet seeing many cases are needed to significantly stem the tide of illness and death in the coming months.

Those are the conclusions of Columbia University researchers who used a New York Times database of known cases and Census Bureau transportation data to model how the outbreak could evolve based on what is known about the virus. The estimates are inherently uncertain, and they could change as America adopts unprecedented measures to control the outbreak.

But they offer a stark warning: Even if the country cuts its rate of transmission in half — a tall order — some 650,000 people might become infected in the next two months.