Photograph: Lucy Nicholson/Reuters

The US’s most influential coronavirus model predicts California will see its outbreak peak this week – exactly one month after San Francisco and several other Bay Area counties enforced the nation’s first shelter-in-place orders. According to the state’s own projections, however, the number of coronavirus hospitalizations and deaths won’t peak until mid- or late May.

“We are not out of the woods yet,” the California governor, Gavin Newsom, said on Tuesday.

So when will California get out of the woods and emerge from the crisis? Since the coronavirus first emerged as a serious threat this winter, epidemiologists around the world have designed several disease models, plotting best- and worst-case scenarios to estimate how many thousands or millions might contract the disease. These projections have informed lawmakers and public health officials and riveted an anxious public.

Unfortunately, none of these predictions can say for certain when the outbreak will fade, epidemiologists say. At best, they are a tool to help officials prepare for a potentially prolonged public health crisis, biostatisticians and infectious disease experts told the Guardian. At worst – they’re entirely useless.

What do the large-scale disease models predict will happen in California?

According to the model developed by the University of Washington’s Institute for Health Metrics and Evaluation (IHME), one of the nation’s most influential and popular coronavirus models, the number of hospitalizations in California will max out on 17 April. The model predicts that the daily death toll in the state will peak two days later. Ultimately, a total of 1,483 Californians will die from Covid-19 by early August, according to the IHME, and nearly 69,000 people will die nationally.

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The model has been tweaked to account for stay-at-home orders, and has more or less matched the reality in California. Its predictions for the number of hospital beds that would be occupied per day were off by fewer than 10 over the weekend.

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But even though it has proved more or less accurate in recent days, “it’s not informed by any epidemiological science,” said Joseph Lewnard, an epidemiologist at the University of California, Berkeley, who specializes in using mathematical and statistical modeling to study infectious diseases. “The model aims to be a crystal ball – and in some sense, that’s dangerous.”

Related: ‘It could have been averted’: How 92 residents at a San Francisco homeless shelter got Covid-19

In statistical terms, the model “fits deaths to a curve”, Lewnard explained – expecting that the trajectory of the disease in California or New York or Florida will more or less resemble the trajectory of other outbreaks in China and Europe, with new infections building up and fading away at a certain rate.

The IHME’s outlook is much rosier than other models, including an initially harrowing projection from Imperial College London, which mapped out a scenario that more than 1 million Americans could die. “If you do the math, that translates to 44,500 deaths predicted in the Bay Area,” said George Rutherford, a professor of epidemiology and biostatistics at the University of California, San Francisco. In reality, there have been about 150 deaths in the region so far. “The takeaway is that shelter-in-place has been hugely life-saving,” Rutherford told the Guardian.

imperial college modelWhat’s up with California’s own modeling?

California’s state officials have based their models on a system developed by researchers at Johns Hopkins University. The model assumes that 10% of Californians with coronavirus will end up in the hospital, and about a third of those hospitalized patients will end up in the intensive care unit.

Increasingly, the predictions have diverged from reality, overestimating the number of people who might become seriously ill. For instance, on 28 March, the model predicted that a median of 5,690 people would be hospitalized due to Covid-19. In reality, 4,362 Californians were hospitalized due to known or suspected infections. On 12 April, California’s model predicted that a median of 10,711 people would be hospitalized with the disease. In reality, 5,048 – less than half the predicted number – Californians with known or suspected infections ended up hospitalized.

“But that doesn’t mean the modeling is wrong,” said William Hanage, and epidemiologist at Harvard University. In some ways, California’s modeling is a bit more dynamic than the IHME model. “It has a mechanism within it that’s trying to account for the impact of different interventions, like shelter-in-place,” Hanage said.

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At the same time, it’s difficult to mathematically map the impact of stay-at-home orders or school closures – modelers have to make educated guesses about how much these measures are actually reducing the spread of disease. Moreover, in a huge state such as California, the models are not able to accurately capture the many local trends. California issued a statewide sheltering order on 19 March, but several Bay Area counties enacted the policy a bit earlier. Newsom limited large gatherings on 11 March. On the 12th, Disney Parks closed and sports events were cancelled.

It could be that California’s model does not fully take into account the impact of those early, piecemeal measures that slowed the spread, Hanage noted. “The way to use models is to think of them as a guide,” he said. “They are possible futures – futures that can change based on the choices we make.”

So, how can we figure out when it’s safe to emerge from isolation?

“As I like to say, all models are wrong, some models are useful,” said Art Reingold, who heads the epidemiology and biostatistics division at UC Berkeley’s school of public health. It’s nearly impossible to divine how many will die, and when exactly the death toll will peak, he noted — the only way to know if California’s outbreak will max out tomorrow, or next month is to wait and see.

In the meantime, public health officials and the general public would do well to pay attention to the actual numbers of hospitalizations and deaths, Reingold added.

“In California, we’re obviously not seeing the kind of dreadful situation we’re seeing in New York,” he said. “And I am optimistic that whenever the peak is, that our early social distancing measures have had an impact, and helped bring down the number of hospitalizations and deaths.”

As the state seeks to ease distancing measures and return to normal operations, testing could be key.

“As we look to reopen, we should have in place a system where we can much more easily, quickly test more people,” Reingold said. “Then we can determine who is infected, isolate those individuals and the people they were in contact with.” Californians could eventually begin to leave their homes more, and slowly reopen businesses, so long as the most vulnerable and more virulent keep safely sequestered, according to Reingold.

Related: California enters ‘optimistic’ phase but coronavirus restrictions won’t ease soon

While the state grapples with test kit shortages and backlogs, “you don’t need to test a lot of people to estimate the prevalence of infections,” said John Ioannidis, an epidemiologist at Stanford University. He and his colleagues at Stanford have been investigating how many people in Santa Clara county, where the university is located, may have developed immunity to the virus – based on the presence of antibodies in their blood.

Strategically testing small groups of Californians across the state could help public health officials understand where the virus has spread and how many people are getting sick. “It’s like in political polling – they don’t call every American and ask if they’re voting for this candidate or that one,” Ioannidis said. “We just need to test representative samples of people around the state and country for the virus.”

Hanage noted that another strategy would be to test one group of people, and everyone they came into contact with, and everybody those people come into contact with, and so on. “That would give you a much better picture of the tree distribution of infections,” he said.

As researchers around the country undertake these efforts, “every day, we’ll have more information,” Reingold said. “However frustrating it is that it’s a slow process, we’re learning a lot.”



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