From a report from The New York Times with Columbia University

In Nelson County, Virginia, if the region or state takes no control measures:
Estimated infection by August 1 would be 81 percent (12,000 people), peaking in late May.

With some control measures:
Estimated infection rate by August 1 would be 69 percent (10,000 people), peaking in mid-June.

With severe control measures:
Estimated infection by August 1 would be 7 percent (1,000 people), peaking after July 31.

From the NYT article: “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…” Read the entire New York Times article