Mathematical models help predict the trajectory of the coronavirus epidemic. But can they be believed?


As Governor Jay Inslee assesses the economic cost of coronavirus closures against the health risks of Washington State residents, at the top of his daily reading list are the latest results from a series of computer models.

Some come from the best universities in the world. Others are of local origin. They are all trying to take a look at the uncertain future and assess the possible paths through a pandemic like no other in modern times.

From state houses to Zoom White House and city council meetings nationwide, mathematical models have rarely been as influential – or debated with such passion.

Experts on the right insist that faulty models have overestimated the danger and led to crippling economic stoppages. Critics of the Trump administration say the authorities are choosing the most optimistic models to minimize the severity of the epidemic and claim credit for reducing the toll. For most people, models are mysterious black boxes. The numbers they spit are constantly changing, creating confusion about their validity and value.

But epidemiologists – and some politicians – say it’s important to understand what models can and cannot do, and the best way to use them at a time when policymakers are largely blinded with so much as yet unknown things about the disease and its prevalence.

“Even with the most intelligent people in the universe – many of whom live right here in Washington State – that doesn’t mean they have a crystal ball,” Inslee said in an interview. “We had to make assumptions assuming that there is a high level of uncertainty. “

Because the tests have been so limited, no one knows how many people are actually infected with the new virus. Asymptomatic people can spread the disease, but with what ease? Does post-infection immunity persist for years or just months? As activities begin to resume, health officials are trying to determine how many tests and contact tracing will be needed to control the disease.

At best, models can take advantage of imperfect knowledge about the new virus to simulate alternative futures and help guide decisions. The driving forces behind them are mathematical approximations to epidemics based on more than a century of experience with infectious epidemics. As new information appears, the entries in the model change – as do the results.

“We are trying to take the best science we have and put this science in motion to reach logical conclusions,” said Daniel Klein, head of the computer research team at the Institute for Disease Modeling (IDM) at Nice view. Washington-based IDM modeling is an important part of the portfolio that Inslee and health officials regularly consult.

It is a mistake to hang your hat on specific numbers generated by models, said Ruth Etzioni, biostatistician at the Fred Hutchinson Cancer Research Center. “It is expecting too much from the models, and you’re going to be disappointed every time,” she said.

What the models do best is to provide rough estimates of potential impacts and compare strategies – such as reopening restaurants, holding large rallies or closing schools. “They won’t be perfect, but they can provide a little lab where you can try different approaches and find out which ideas are good or bad and which could be better,” said Etzioni.

An expression that has become almost as common as “flattening the curve” these days is attributed to the late statistician George Box: “All the models are wrong, but some are useful”.

Without models, leaders confronted with a new pathogen would be forced to proceed by intuition, or by trial and error – with very high stakes.

“If we didn’t have models, the alternative would be guesswork or a finger in the wind,” said Klein. He and his colleagues are now focusing on the issue that concerns everyone: how to reopen safely while minimizing new infections, hospitalizations and deaths.

At the start of the pandemic, modeling galvanized action. Projections that more than 500,000 Britons and 2 million Americans could die if the virus were not controlled have prompted leaders of both countries to impose bans. But when modelers at Imperial College London reported significantly lower death projections due to restrictions, the new figures were widely misinterpreted to mean that their original results were wrong.

When modeling triggers an action that changes the course of an epidemic, it may appear that the modellers were ridiculously out of base, said Dr. Georges Benjamin, executive director of the American Public Health Association.

“You have to anticipate that and make sure people understand that the numbers are going to change, and that is what success looks like,” he said.

Different models are designed to answer different questions, but modelers are often not transparent about the limits of their approach and assumptions, said Etzioni – who would like to see the equivalent of a nutrition label on each model stating this information in simple language.

The workhorse of epidemiological modeling is an approach that classifies members of a hypothetical population according to whether they are susceptible to a new disease, infected, cured – and therefore immune – or killed. Researchers make their best biology assumptions based on what has already been learned, run the model, and then see how well it matches recorded deaths or other real benchmarks.

This is the approach IDM used to estimate the “effective reproductive number” – the number of people to whom each infected person transmits the virus – in the Puget Sound area. At first, the number was between two and three. Thanks to social remoteness, he seems to have fallen below one – a key tipping point which means that the number of cases should decrease steadily.

“These types of epidemiological models are hardened in battle,” said Etzioni. “They have been used successfully several times in the past.”

But another Seattle-born model takes a different approach – and has come under heavy criticism. The University of Washington Institute for Health Metrics and Evaluation (IHME) does not include any information about the virus in its model. Instead, the researchers report the number of deaths in countries and states where strict social distancing has been implemented and assume that deaths in other places will follow similar trajectories.

IHME director Dr. Christopher Murray defends the approach, which he says doesn’t require assumptions about transmission rates or other biological parameters. The group regularly posts updates to a website that forecasts daily and total deaths and peaks in hospital for each state and dozens of countries.

Murray has frequent talks with some of the best lawmakers and members of President Trump’s coronavirus task force, but critics say the model promises more than it delivers.

“The appearance of certainty is attractive when the world is desperate to know what awaits us,” wrote a group of epidemiologists in a review that raised concerns about the “validity and usefulness” of projections from the world. ‘IHME. The methodology of the model makes it volatile, with forecasts of deaths that exploded in certain places within a few days, said the group.

Initial results for Washington predicted more than 1,400 deaths early in the summer, which were reduced to 600 10 days later. As of Friday, the IHME model predicted a total of 877 deaths across the state in early August. This is far less than the 1,651 deaths projected by an MIT model which is also part of Inslee’s daily review.

One of the biggest criticisms of the IHME model is that its main assumption – that social distancing will remain in effect everywhere until the start of the summer – is unrealistic and should lead to overly optimistic prospects.

With other models projecting more than 100,000 deaths in the United States, the IHME estimate in early April that the virus would kill 60,000 Americans by August was cited by the Trump administration as evidence that the pandemic would not be as serious as we feared. But the country crossed the 60,000 mark last week.

IHME coronavirus modeling started as a way to help UW Medicine prepare for the next influx of patients – and it was extremely helpful, even if the initial predictions were far worse than reality, said Lisa Brandenburg, who is in charge of all UW hospitals and clinics. Initial model runs have suggested that the maximum number of COVID-19 patients in a single day could be between 236 and 950. Administrators have prepared for the worst-case scenario.

The actual number of hospitalizations at UW facilities peaked at 122. But Brandenburg does not regret the decision to prepare for a disaster, even if that meant putting all other patient care on hold and a big financial blow. The IHME’s shocking projections helped persuade state and local leaders to impose restrictions to stem the virus, and they certainly saved lives, she said.

“Yes, I wish I had a more perfect vision. But I also don’t think we could have made any other choice with the data we had at the time, “she said.

However, with the possibility of a new wave of coronavirus cases in the fall, Brandenburg said it plans to check out a range of models instead of just one – a hedge that is universally recommended by modelers themselves. same.

As health officials try to anticipate what will happen when the restrictions are lifted, another type of model is beginning to play a prominent role. Similar to standard epidemiological models, these “agent-based” approaches are much more detailed and sophisticated. People are treated as individuals and communities can be simulated to the census tract level, with realistic approximations of social interactions and modes of travel.

It’s like playing the SimCity computer game, with contagion taken into account – and it requires such computational power that Google gives access to its cloud capabilities.

This granularity is necessary to answer what are now the most pressing questions, said Dr. Elizabeth Halloran, a disease modeller at The Hutch. Questions like: when can children go back to school? And what is the most effective way to extend testing and contact tracking to prevent the virus from spreading?

“These models allow you to understand the complexity,” said Halloran.

She works with a group at Northeastern University whose powerful model is already trying to find answers. One of their most recent simulations suggests that even a relatively modest test regimen, aimed only at people with obvious symptoms, could be effective when combined with modest levels of contact tracing. Only about 7% of the population should be isolated at some point, while everyone could resume their normal life.

But this is just a set of simulations, from a model.

“You start to encrypt things and people think they are true,” warned Halloran. “Nothing on any model is true. “

The models to which Inslee is paying the most attention are currently pointing in different directions. While IHME projects a sharp decline in infections and deaths, IDM projects a much slower decline. The governor hopes the forecasts will converge as more data arrive. But so far, the main point of agreement has not been pleasant, he said.

“The most important thing that we have learned from the models – and it is unfortunate – is that they are convinced that if we eliminated all social distancing at the moment, the pandemic curve would increase quite dramatically, quite quickly.”

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