For the first time in weeks, there are signs that Italy may be over the hump in battling the Covid-19 coronavirus.

The entire country remains on government-ordered lockdown, but on Monday officials said that the number of new cases and deaths had declined for two days in a row.

Recent reports show nearly 64,000 confirmed cases of Covid-19 in Italy and more than 6,000 fatalities. More than 600 people died on Monday — yet that was the smallest increase in several days.

“We can say that today is the first positive day,” Giulio Gallera, top health official in the hard-hit region of Lombardy, told the New York Times.  “It’s not the moment to sing victory, but we finally see light at the end of the tunnel.”

That’s the good news.

Now for the bad news: the Italian medical system is still overwhelmed. Hospitals are filled beyond capacity, there’s a severe shortage of respirators for the sickest patients, exhausted doctors and nurses are forced to choose between those they might save and those they can’t.

On top of all this, in some localities, 25% or more of health workers are themselves infected and in quarantine.

Lombardy, in north-central Italy, and its capital, Milan, may be seeing the worst of the pandemic.

In a paper published over the weekend, doctors from a hospital 25 miles northeast of Milan said that “70% of their intensive care unit beds were reserved for coronavirus patients with ‘a reasonable chance to survive,’” the Times reports. “Older patients, they said, ‘are not being resuscitated and die alone.’”

Health workers are encouraging even people with severe symptoms to stay home. The most heavily infected areas “have now essentially moved beyond testing,” the Times says.

“Right now in Lombardy the contagion is so widespread that we should consider every person potentially positive,” said Roberto Burioni, a prominent virologist in Milan.

What’s happening there is (or should be) of special interest to Americans, because the U.S. is “lagging only days behind Italy in the progression of the pandemic,” the Times says.

Luca Zaia, the president of Veneto, another north Italian region hit hard by the outbreak, warned that any country facing the outbreak needed to prepare, and said that Americans should “buy all the mechanical respirators possible to save the lives of these patients.”

For all of Italy’s tragedy, there were occasional signs of hope, like a 95-year-old grandmother, widely reported on Twitter as having survived the virus.