Italy has reported more than 132,000 coronavirus cases and more than 16,000 deaths, but that's likely an underestimate, as only people who die in hospitals are counted in the national tally. Others at home or in nursing homes may not have been tested for COVID-19 at all.

At one nursing home in Nembro, a town in northern Italy, 33 people have died since the outbreak began. They include Agnese Magoni, a housekeeper who loved walks in the garden, and Giulio Bonomi, a carpenter and bookworm.

They died of COVID-19, doctors say, but they weren't tested before they died, so they don't appear in the country's death toll. The virus struck so hard and so fast at the nursing home, those infected never made it to a hospital.

Dr. Barbara Codalli called what happened at the nursing home a "tsunami." A tsunami that killed three residents per day at its peak and could still strike the 52 surviving residents, she told CBS News foreign correspondent Chris Livesay.

Those residents have still not been tested, Codalli said.

"Neither have we," she told Livesay. "I might have COVID too. Two coworkers have died, and many others are home sick."

Untold victims also have died at their homes, untested and uncounted, like Alessandro Boromelli. Police were seen collecting his oxygen tanks, now in short supply.

"This disease is wiping out the generation that built everything around us," his son, Valerio Boromelli, said.

Boromelli said his father and no one in their house was tested for COVID-19.

The official number of deaths in Nembro attributed to COVID-19 is 31, according to an article co-written by the town's mayor, Claudio Cancelli. But, he estimated the real death toll is much higher.

"According to our analysis, it's four times higher. Most deaths simply aren't counted," Cancelli told Livesay.

Underreporting the deaths isn't just happening in Nembro. Mayors across Italy are sounding the alarm, warning COVID-19 is even deadlier than we think.