While the improvements continue almost daily in New York and other areas on the East Coast hit hard by the early impact of the Coronavirus, new numbers clearly show the virus outbreak now shifting its way across the United States, infecting other areas which had escaped major virus troubles in March and April.

Over the weekend, a series of states hit highs for their 7-day average of new virus cases, with warning signs in Texas, North Carolina, South Carolina, Arizona, and other states.

"There is persistent spread," Dr. Scott Gottlieb told CNBC on Monday. "We have about 20,000 cases a day, and it's not going down."

"The point is, we still have an epidemic that is very slowly expanding in this country," Gottlieb added.

The picture is much different in areas between Washington, D.C. and Boston, as the big urban corridor anchored by New York City begins to finally loosen virus restrictions.

For example on Monday in Maryland, the number of Coronavirus hospitalizations dropped below 1,000 for the first time since April 10.

On Monday, Massachusetts was moving into Phase 2 of its re-opening.

"This next step will allow more businesses and activities to resume operations," said Gov. Charlie Baker (R-MA).

Last week, New York City had its first day without a Coronavirus death since March.

"Day 100 since we had the first case in New York," said Gov. Andrew Cuomo. "It is a day that New York City begins to re-open."

While New York is seeing lower case numbers and deaths, the increase in Coronavirus cases around the nation isn't happening mainly because of individual prison or meatpacking plant outbreaks - but rather it is taking place in big counties which anchor urban areas.

Numbers compiled by the Washington Post for example show a sustained increase over the last two weeks in Maricopa County, Arizona (Phoenix), Los Angles County in California, and the three big counties of South Florida - Palm Beach, Broward, and Miami-Dade.

Meanwhile, hospitalizations have hit a high in Texas, and in North Carolina, while South Carolina, Utah, and Oregon also hit their highest 7-day case average on Monday.

On Monday - a day which usually features low reporting of new cases and deaths - Arizona reported 789 new cases of the Coronavirus, over triple the previous high for any Monday since the virus outbreak began in March.

The jump in states like Arizona was noted on Monday by Gov. Cuomo, who used a slide at his daily briefing to tell New Yorkers to, “Stay disciplined.  Stay smart.”

Under that headline, Cuomo showed graphs demonstrating the increase in virus cases in Arizona, California, Texas, and Florida to hammer home his warning.

“That is the cautionary tale, my friends,” Cuomo said.