By David H. Montgomery, Minnesota Public Radio News

When Gov. Tim Walz announced another month of a stay-at-home order for Minnesota this week, he talked repeatedly about one of the pieces of evidence spurring the order: the state’s “model” of the COVID-19 outbreak.

What exactly is this model? It’s a complex mathematical equation that estimates the impact of a disease under different scenarios. Models are a standard practice in epidemiology, but have assumed newfound prominence in 2020 as they guide governments to impose massive disruptions to everyday life in an attempt to manage the spread of COVID-19.

Many states, like Minnesota, have their own models to guide policymaking, as do federal agencies and some researchers. Minnesota’s model was constructed by a partnership between the state’s Department of Health and the University of Minnesota School of Public Health, and is currently in its second version.

Most details of Minnesota’s model remain secret, and will be for weeks to come. But state health officials on Friday unveiled some aspects of how it works. Here are key things to know about the model:

It relies on a number of estimates

Since not everyone is being tested, the model must estimate the number of positive COVID-19 cases in Minnesota, the number of intensive care unit beds patients will require, and the number of people who will die from the respiratory illness.

It does this based on a few different factors. First, it needs inputs about the disease itself beginning with how many people will get sick. To figure this out, the people running the model estimate how likely a sick person is to infect others, which in turn is affected by factors such as how many people will be asymptomatic carriers, and how long it takes for a person to become contagious once they’re infected.

Second, the model needs an estimate of the severity of the disease: Of those who get infected, how many will need to be hospitalized, how many will need intensive care beds, and how many people will die?

These estimates vary by age. The elderly are far more likely to have severe symptoms and die than people in their 20s. So, the current model estimates that just 1.2 percent of people 20 to 29 who catch the disease will need hospitalization, versus 27.3 percent of people over 80.

Third, it looks at available resources, especially the number of ICU beds. If someone is so sick they need a ventilator to breathe, but can’t get one, they’re extremely likely to die. So, the death rate would be expected to increase when there are fewer ICU beds.

All these factors — how many people get sick, how serious the disease is and how many resources are available — produce predictions about how many people will get sick from COVID-19 and how many will die.

Crucially, the model has to predict when these illnesses will happen. That’s important because if lots of people get sick all at once, they could overwhelm hospitals’ capacity to treat them. But if the illnesses are spread out, there could be enough beds.

What the model predicts right now

The model makes several predictions, depending on what policies Minnesota enacts. For example, one scenario assumes business-as-usual; another considers what would happen if Minnesota continues physical distancing into the summer. These scenarios are drafted by the scientists running the model, and don’t necessarily match up with the policies Walz and state lawmakers ultimately enact.

Under the model, scenarios affect both how many people get sick, and when those illnesses happen. For example, encouraging vulnerable Minnesotans to keep their social distancing into July could lower the peak demand for ICU beds by nearly 1,000 compared to a scenario where all Minnesotans return to normal in May.

The model estimates that Walz’s decision to extend the stay-at-home order into early May will likely delay that peak by a month or more, which officials have said could buy time to build more ICU beds to meet the demand.

The model also predicts that even with vigorous public policy responses, the toll of COVID-19 on Minnesota will be extreme. For example, even with a stay-at-home order into May and social distancing into June, the model predicts that 22,000 Minnesotans will die from COVID-19 over the 12 months from March 2020 to March 2021. That would be an increase of more than 40 percent over Minnesota’s normal death rate, although how many of those predicted deaths due to COVID-19 would have occurred anyway due to other causes is unknown.

Alternative scenarios with less stringent measures, per the model’s predictions, would be even more devastating, with 40,000 to 50,000 deaths.

How certain is the model?

Minnesota’s COVID-19 model is based on extensive modeling of past diseases and the latest information about COVID-19 itself, but it’s far from precise. All its predictions include a pretty wide range of probable outcomes.

The peak demand for ICU beds, for example, could be as low as 2,000, or as high as 6,000, depending on the scenario.

That’s a huge range, and where the demand ends up could have major consequences. Walz said this week that Minnesota has just over 1,000 ICU beds currently, and could get to a total of nearly 3,000 within 72 hours. Those nearly 3,000 beds could be enough to handle an outbreak on the low end of the model’s predictions, or fall drastically short of an outbreak on the upper end.

This kind of margin of uncertainty exists for every one of the model’s predictions, from the timing of the outbreak’s peak to the number of dead. That prediction of 22,000 COVID-19 deaths, for example, is actually just a midpoint between a high estimate of 36,000 dead — an 80 percent increase on Minnesota’s normal death rate — and 9,000 dead — a 20 percent increase.

“Every assumption, every data point … has some uncertainty related to it,” said Stefan Gildemeister, the state’s health economist.

How the model changes over time

Minnesota’s “model” also isn’t a single calculation. Rather, the state is constantly putting new data into it, producing different results.

The first version of the model, in March, was based primarily on data from China, where the COVID-19 outbreak began. The second version, unveiled Friday, includes data from the early stages of the outbreak in Minnesota, as well as the disease’s progress in Europe.

Those new sources of data had two big effects: They increased their estimate of how infectious COVID-19 was, and lowered their estimate of how much time sick patients would need in ICU beds.

And this week’s update won’t be the last.

“I fully expect that our understanding of the disease will change every week,” Gildemeister said.

How the model informs policymaking

Physical health is not the only consideration Walz and legislative leaders have to ponder as they decide how long Minnesotans will have to stay at home and other weighty factors.

For example, one major factor the model doesn’t consider is the economic impact of mitigation measures such as a stay-at-home order, which has left more than 10 percent of Minnesota’s work force unemployed so far.

The model can produce estimates of the health impact of the disease. But policymakers have to decide how much to weigh that against the economic cost of social distancing.

What we don’t know

The Department of Health and University of Minnesota teams behind Minnesota’s COVID-19 model have shared what the model predicts, and some of the details about what goes into it. But what happens in between remains in a black box.

The actual code for Minnesota’s model is a secret, leaving Minnesotans to trust that hugely consequential decisions about their lives and jobs are being made based on reliable numbers and processes.

Some other COVID-19 models, such as that of the Institute for Health Metrics and Evaluation at the University of Washington, have publicly released their code.

The state says it intends to eventually release the code, but not until late April. The exact reasons why the code can’t be released until then aren’t clear. Walz suggested on Monday that part of the model was based on “proprietary information that the researchers over at the University of Minnesota have.”

On Friday, Gildemeister said he had concerns that models that let anyone use them might be “irresponsible” because “it allows folks to make assumptions that aren’t very realistic ones.”

These concerns, and the lack of details so far, have stirred up critiques from lawmakers and citizens alike, especially because the model’s prediction of dire health consequences has justified major economic disruption.

State Sen. Karin Housley, R-St Marys Point, criticized Walz on Twitter Friday about the model’s “secrecy.”

“The U of Washington has had their model online for over a month!” Housley wrote. “We’ve shut down thousands of businesses due to your modeling … why the secrecy?”