In the last few weeks, we’ve all become a little more familiar with epidemiological models. These calculations, which make estimates about how many people are likely to get sick, need a hospital bed or die from coronavirus, are guiding public policy — and our expectations about what the future holds.

But if you look at the models, they don’t really agree.

U.S. coronavirus deaths in five different forecasts Reported deaths are rolling 7-day averages. Lines differ on whether to include roughly 5,000 probable deaths in New York City. Latest model projections for Northeastern, I.H.M.E. and M.I.T. are April 21; Columbia is April 19; Imperial is April 13.

The chart above includes five leading models’ predictions of U.S. coronavirus deaths through May 30, most of them standardized and compiled by a team at the University of Massachusetts Amherst.

You’ll see differences in how high the peak of deaths is likely to get, and in how far we are from such a peak.

Most of the models shown above predict that the country is currently past or near the peak number of deaths for this wave of the epidemic, assuming current restrictions aren’t relaxed. But they estimate a range of total deaths — 60,000 to 100,000 — through May 23.

These models use different techniques to project the future. But most of them share an important basic assumption: They are built around the notion that the current regimen of stay-at-home orders and social distancing will continue. And almost all of them cut off their predictions after two months or less, even though epidemiologists believe that the coronavirus pandemic will be with us for far longer.

However good the modelers’ mathematical strategies may be, many of the descriptive facts about the virus are still unclear. Researchers aren’t sure about the rate at which people who become infected die, or about the rate of transmission to other people. They don’t know for sure how many people have already been infected and have some immunity to the disease — or how long that immunity will last. Even the count of coronavirus deaths itself is uncertain.

In addition to the usual challenges, the models have recently been asked to contend with a large revision in the number of deaths believed to be caused by coronavirus in New York.

Several epidemiologists said it was hard to expect the models to offer precise forecasts at this point because they rely on such uncertain inputs. “It’s like trying to repair a car while it’s still running,” said Andrew Noymer, an associate professor of public health at the University of California, Irvine.

The range of possibilities in projections of death can be large Reported deaths are rolling 7-day averages. Lines differ on whether to include roughly 5,000 probable deaths in New York City. M.I.T. calculated confidence intervals, but chose not to include them.

The model most frequently cited by the White House is from researchers at the Institute for Health Metrics and Evaluation at the University of Washington. It makes its estimates by comparing the recent trajectory of the coronavirus in the United States with those of countries further along in their epidemics. That method allows them to estimate a trajectory without having to know too many facts about the disease itself. This model has tended to be less pessimistic than the others about the next few months; the White House has cited its estimate of around 60,000 deaths over the next few months. Epidemiologists have been loudly and publicly critical of its design.

The other models, including those from Northeastern University and Columbia University, which are built on epidemiological theory, use estimates about how contagious the virus is, how long it takes for people to recover, and what share of infected people with different risk factors will develop a serious illness or die. In theory, such methods are more precise, because they are built around the ways that diseases actually spread and kill people in different circumstances. But because these models all rest on a shaky foundation of knowledge about the virus, several of them have also conflicted with recent death counts, and their projections vary.

“We want them to provide more information than they can,” said Jeffrey Shaman, a co-author of the Columbia model, who said the models were still valuable in showing a range of what could happen. “We have uncertainty on top of uncertainty on top of uncertainty.”

But they remain the best guide as policymakers and hospital executives try to plan for how many hospital beds or ventilators — or how much morgue capacity — they need. That doesn’t mean the models have been as useful as policymakers would like: New York relied on models that told it to create far more bed and ventilator capacity than it has turned out to need.

Researchers at the Los Alamos National Lab have released a model with state-level predictions that assume social distancing interventions will continue. Their predictions for New York State include a broad range of possibilities, including cumulative totals of less than 25,000 deaths and more than 60,000 deaths by the end of May. Four of the other modelers are publishing estimates for individual states as well as the nation as a whole.

New York State coronavirus deaths in five different forecasts Reported deaths are rolling 7-day averages. Lines differ on whether to include roughly 5,000 probable deaths in New York City. Los Alamos model available only at the state level. Columbia, Los Alamos and Northeastern include 80% intervals. I.H.M.E. shows a 95% interval. M.I.T. calculated confidence intervals, but chose not to include them.

Nicholas Reich, a biostatistician who runs a seasonal flu forecasting lab at the University of Massachusetts Amherst, said it was important to collect outputs from all the models, because of the uncertainty around all the projections.

“If you’re just looking at one model, you’re not seeing the full diversity of what could happen,” said Mr. Reich, who leads the team that aggregated the data.

How the different projections of U.S. deaths have changed over time Models as of... Reported deaths are rolling 7-day averages. Lines differ on whether to include roughly 5,000 probable deaths in New York City.

A review of all these models shows how much they are adapting to new information. The projections change, as new death counts and public health research bring them closer to understanding how the disease, and the people it affects, are behaving. Most of the projections have reduced their expected number of cases and deaths in the coming weeks.

Although some politicians like to treat the models as precise, all of them include large bands of uncertainty around their principal projections. In some cases, the real numbers have ended up outside these ranges more often than they should, a sign that the modelers have underestimated how little they know.

Samuel Clark, a demographer at Ohio State University, says he has been closely watching the model from Imperial College London for a sense of how the epidemic might respond to different scenarios, but he does not currently expect any of the models to function like crystal balls.

“They’re basing their model on very few data, and because of that you have very large uncertainty,” Mr. Clark said.

Errors may come from methodological flaws in the models. And they may come from errors in assumptions about the disease, like its fatality rate. But they may also come because no mathematical model can be sure what actions governments and individuals will take in the face of a prolonged epidemic.

Currently, most states have imposed some form of stay-at-home order, and several cities have required people to wear masks when they work and shop. Those kinds of measures are designed to slow the spread of the virus, to achieve a reduction in cases and deaths that all of these models expect.

But the White House has already begun preparations for states to loosen such restrictions once the cases get low enough. Once behavior changes, the spread of the disease is likely to change too, meaning all the models will need to recalibrate. The teams from Imperial College London and Northeastern University release projections only about a week into the future, because their researchers worry that policy and norms could change quickly.

The Columbia University model tries to anticipate those different possible futures. In our charts above, we showed the output of the middle scenario of the range. But the model has three outputs, based on different estimates of how much governments and people will work to reduce social contact when they see an increase in confirmed cases.

Reported deaths are rolling 7-day averages. Lines differ on whether to include roughly 5,000 probable deaths in New York City.

Dimitris Bertsimas, a co-author of a model from the Massachusetts Institute of Technology, said his team had declined to make very long-term predictions, given the policy uncertainty.

“We are reasonably certain until approximately June 15 there will be significant measures” to contain the spread of the virus, said Mr. Bertsimas, an associate dean of business analytics at M.I.T.’s Sloan School of Management. “After that, God knows.”