That's what places like New York City are discovering after months of steady progress in fighting the pandemic.

And this is a very bad time to be going backward, as Americans face a trio of major challenges this fall: more indoor gatherings, a potential coronavirus-and-flu "twin-demic," and trying to get or keep students back in school safely.

Nationwide, 21 states reported more new cases this past week compared to the previous week, according to data from Johns Hopkins University.

Only 10 states are showing downward trends in new cases -- Arizona, Florida, Georgia, Tennessee, Virginia, Connecticut, Vermont, New Hampshire, Delaware and Maryland -- and 19 states are holding steady.

Track the virus in your state and across the US

But in many states, "it's not only that the number of infections keeps on going up. It's also that the test positivity rates are trending in the wrong direction," emergency medicine physician Dr. Leana Wen said Monday.

A test positivity rate is the percentage of test results that turn out to be positive. The World Health Organization has recommended test positivity rates stay at or below 5% for at least 14 days before businesses reopen.

"We're seeing more than a dozen states with a test positivity is over 10%. And there are two states -- Idaho and South Dakota -- where the test positivity is over 20%," Wen said.

"That means that not only do we have increasing infections in these states, we also don't have nearly enough testing."

Cases 'grow at an alarming rate' in parts of NYC

For the first time since early June, New York state reported more than 1,000 new cases Saturday -- prompting Gov. Andrew Cuomo to warn that this virus "remains a force to be reckoned with throughout the country."

"It's vital that New Yorkers continue to practice the basic behaviors that drive our ability to fight Covid-19 as we move into the fall and flu season," Cuomo said. "Wearing masks, socially distancing and washing hands make a critical difference."

In New York City, Covid-19 cases "continue to grow at an alarming rate" in eight neighborhoods in the city, outpacing the citywide average by 3.7 times over the past 14 days, the city health department said Monday.

In response, the department said it will deploy 11 mobile testing units this week to areas with high positivity rates and triple the capacity of "express" testing sites in some areas.

New York state was once the US epicenter of this pandemic, but the rates of new cases, hospitalizations and deaths have plummeted in recent months.

The decreases came after New York shut down and mandated masks in public early. The state also ramped up testing capabilities on its own when testing was scarce nationwide.

New York state boasted a test positivity rate of less than 1% for more than a month. But that streak has been broken, with the test positivity rate hovering around 1.02% in recent days.

"We cannot drop our guard," Cuomo warned.

That's especially true as public schools in New York City reopen to students this week. But officials could decide to close s

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