The defenses kept Hong Kong’s daily COVID cases to the single digits for most of the pandemic. Even then, the city’s “dynamic zero-COVID” strategy—the preferred terminology among Hong Kong officials for the policy to eliminate infections—drew criticism for humanitarian concerns, such as when children as young as 1 were separated from their parents and isolated in hospitals or quarantine camps. Now an Omicron outbreak is driving record infections—3,629 on Friday—prompting the city to delay the election from March 27 to May 8.

“The cases have far exceeded our capacity in every respect,” Carrie Lam, Hong Kong’s current chief executive, said in a press conference on Friday, estimating that the city’s current wave will not subside for two to three more months. “We believe the peak is yet to come.”

But officials remain intent on isolating every single case.

To pull off the feat in a city known for its density, officials are pursuing increasingly desperate measures—such as putting tens of thousands of COVID-19 patients in hotel rooms or on a cruise ship—to try to quash an outbreak that’s already out of control.

At the very least, Hong Kong has abandoned its effort to hospitalize every COVID case. On Sunday, the government started triaging cases after patients with asymptomatic and mild infections overran the city’s hospitals.

“At this critical moment we need to preserve our limited resources for patients who are most in need,” Larry Lee, a top city health official, said on Sunday.

The move did little to immediately ease the overflow. Hundreds of COVID-19 patients spent the night on cots outside full hospitals. Doctors say patients with mild infections are still inundating their facilities and that the government is not doing enough to prioritize care for the most severe cases.

“The hospitals are currently overcrowded partly because we have admitted people who don’t really need to be there,” Dr. David Owens, a physician in the city and honorary professor at Hong Kong University’s medical school, wrote in a blog post on Thursday.

Even if the government has given up on hospitalizing every patient, it still aims to isolate every case. There’s now a backlog of over 22,000 people who have tested positive for the virus but are waiting for quarantine facilities, reports the South China Morning Post.

In short, Hong Kong—known in the best of times for its nano-apartments and über-expensive real estate—has run out of space.

Earlier this month Hong Kong converted Penny’s Bay, a government-run quarantine camp, from housing close contacts of COVID cases to instead isolating confirmed infections. But the camp’s 3,500 beds quickly filled up, pushing officials to seek other solutions.

This week, some local lawmakers suggested that mild infections could quarantine on vacant cruise ships, which are not operating owing to the city’s COVID-19 restrictions. On Friday, the South China Morning Post reported that the government may convert Kai Tak Terminal, a now-deserted cruise ship terminal, into an isolation ward for tens of thousands of COVID patients.

“If there is an urgent need, the sector is happy to see cruise ship terminals being turned into quarantine facilities,” Yiu Pak-leung, a lawmaker focused on tourism, recently told local media.

Meanwhile, Hong Kong property companies and hotels said this week that they would make over 20,000 rooms available to quarantine patients and close contacts. Officials are also set to decide on a proposal in coming days to expand Penny’s Bay’s capacity to 9,000 beds.  

But public health experts warn that Hong Kong will not be able to make enough rooms available to isolate all infections, especially if Hong Kong embarks on a plan to test every resident in the city in March.

Short of a citywide lockdown, Hong Kong’s current Omicron-fueled outbreak is “unlikely to be containable,” the city’s leading infectious disease research center at Hong Kong University wrote in a study published this week. The study projected that Hong Kong’s COVID count will peak at 28,000 cases per day by late March if the city keeps its current public health measures in place.

Meanwhile, Owens and other experts believe that Hong Kong’s resources may be more effective if deployed to improve the city’s lagging vaccination campaign instead of finding new quarantine facilities.

“The vast majority of people can be managed at home,” Owens wrote.