“All of the available information strongly suggests that social distancing policies are making a big difference,” said Dr. Greg Roth, a clinical adviser to the team running the model at the University of Washington, one of the most prominent sources of disease data.

“We’ve seen the shape of the death curve in places like New York and Italy sharpen to a much sharper peak.”

But social distancing directives came late in Texas, Florida and some other Southern states, where hospitals also have less capacity. Big spikes in those states, especially if they occur at the same time, could push death numbers higher if hospitals are overwhelmed and if older and more vulnerable patients, particularly in Florida, account for high numbers of cases.

The models used to predict sickness and death vary widely and are admittedly faulty, given that they rely on specific assumptions about what people and governments are doing to stop the disease’s spread.

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The Institute for Health Metrics and Evaluation – one of the main sources the White House used to inform its numbers – includes data from Wuhan, China, where the government imposed a strict lockdown, isolated infected people from their families and employed thousands of workers to identify and track infected people to quarantine them and monitor their contacts.

That model has incorporated American health statistics but assumes even the states that have been slowest to adopt stay-at-home orders will do so within seven days.

As recently as mid-March, top Trump administration officials warned that Italy, where thousands of people were dying and hospitals were overwhelmed, was a worst-case scenario, urging Americans to wash hands and stay home to emulate the success of South Korea in combating the spread of the virus.

But botched US testing and a slow and uneven response by the Trump administration had by then already made the South Korean model impossible for the United States to emulate.

Now Italy, the one-time cautionary tale, has become the goal. Over the weekend, Dr Deborah Birx, the White House coronavirus response coordinator, spoke of “hopeful signs in Italy and Spain, where we see, finally, new cases and deaths declining”.

“It’s giving us hope of what our future could be,” she added.

Jeremy Konyndyk, who led the overseas Ebola response for the Obama administration, said the shift in rhetoric shows how “the goalposts have moved” in just a few weeks. But he said Italy would “be a welcome outcome” at this point, “given how bad things have gotten” in the United States.

“We’re going to have hotspots everywhere,” he predicted.

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Public health experts believe Italy may be nearing the end of its outbreak, with reported deaths and new cases declining in recent days. The country, with roughly a fifth of the US population, recorded 17,127 Covid-19 deaths as of Wednesday, which would translate to roughly 85,000 deaths in the US population.

New York’s disease cluster, the epicentre of the American outbreak for weeks, is also showing signs of ebbing. San Francisco, another dense city with an early outbreak, also has seen better than expected results.

Public health experts say the outbreaks in Italy and New York ultimately could look relatively benign.

Italy has more hospital beds and doctors per capita than the United States, and the outbreak centred in Italy’s more prosperous northern region. And even as New York City’s dense population and busy subway system helped the virus spread easily there, the city has several advantages over other parts of the United States.

New York has more large and well-resourced hospitals, and its governor was early and aggressive in imposing stay-at-home measures. New York also attracted help from around the country, in part because it was the first state to be hit hard and also because it is the nation’s financial and media capital.

Governor Andrew Cuomo’s updates, including his frequent pleas for help, have been broadcast nationally on a daily basis, putting pressure on the Trump administration and attracting physicians and supplies from around the country.

If other hotspots develop simultaneously – say in Dallas, Miami and Phoenix – it is not clear that they can expect the same level of help, especially if other states are beginning to see spikes in patients at the same time.

“Will 49 other governors be able to do what Cuomo has done?” asked Dr. Ashish Jha, who directs Harvard University’s Global Health Institute.

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Jha said the number of factors involved in the next phase, including how many Americans practice social distancing, makes the modelling a “tea-leaf reading” to some extent.

The effort is also hampered by the lack of reliable government data and adequate testing, which makes it difficult to know how many Americans have been infected and what the true death rate is.

Many people who died of Covid-19 were never tested, meaning they will not be reflected in the death toll. Other people who carry the virus show no symptoms and are also not counted. But if that number is high, it means more Americans could spread the disease once social distancing ends.

Scientists are also still learning about the virus, including the length and level of immunity people get if they are infected.

Other types of coronaviruses have immunity that lasts a year or two, but the verdict is still out on this one, said Dr. Chris Beyrer, director of the Johns Hopkins Training Programme in HIV Epidemiology and Prevention Science.

Beyrer said Europe, where most countries have a national health system, is in better shape to track patients who have been infected.

A longer immunity period would give scientists more time to develop and circulate a vaccine, a crucial step toward limiting deaths when Americans return to work and socialising, and when and if second and third waves of the pandemic occur.

The Trump administration has only committed to recommending Americans stay at home until April 30. The Institute for Health Metrics and Evaluation assumes such measures will remain in effect for at least a month longer, and public health experts have still not settled on a recommended timeline.

“One of the concerns is that a large proportion of the population will not have been exposed to this virus” by then, said Roth. “There is a real risk of recurrent local epidemics.”