There’s no crystal ball for modeling the pandemic

Mathematical modelers explain challenges, limitations of their work to predict COVID-19 outcomes
An illustration showing interconnected people
While models can point to key variables that could slow the spread of SARS-CoV-2, modelers caution against expecting them to predict the exact numbers of cases of COVID-19. Getty Images Illustration

Dr. Laura Matrajt didn’t expect to make much noise on Twitter. She just wanted to clarify a term she’d seen sowing confusion on social media.

It was mid-March 2020, and the term was “flattening the curve.”

“I was seeing people in my social media discussing, ‘Is it useful? Is it not useful?’” she said. “Some were saying, ‘People are exaggerating, [SARS-CoV-2] is just like the flu.’”

Matrajt, a mathematical modeler in the Biostatistics, Bioinformatics and Epidemiology, or BBE, Program in the Vaccine and Infectious Disease Division at Fred Hutchinson Cancer Research Center, had been working remotely since the Hutch activated its mandatory remote work policy on March 4.

She spent her days working on a model designed to help optimize cholera vaccine distribution but, over the course of a few evenings, turned her attention to the recently declared COVID-19 pandemic. Matrajt assembed a simple model that showed how much reducing contact — or distancing — by different groups could theoretically change the number of people infected with the novel coronavirus.

She modeled what could happen if no one distanced, if only adults over 60 distanced, if adults over 60 distanced with children, if all adults distanced, or if everyone took steps to reduce contact with others.

The point of her graph was not to project specific numbers, but to show the differences among the various scenarios.

“I just wanted to put it on Facebook so that people understood their particular actions would have a consequence,” she said. This was the early days of the pandemic, before many had accepted that social distancing could help slow the new virus’ spread.

First, Matrajt posted her graph on Facebook, and then, on the recommendation of a friend, on Twitter. It took off.

“I was not expecting people to be so interested in this,” she said.

It was the first inkling Matrajt had that mathematical modelers like herself might experience this pandemic a little differently.

A woman with dark hair and a raspberry-colored sweater
Dr. Laura Matrajt Photo by Robert Hood / Fred Hutch News Service

Overwhelming early days

Dr. Josh Schiffer, a Hutch infectious disease specialist who develops models of viral dynamics in infected people, reckons that prior to the SARS-CoV-2 pandemic, he’d spoken to news media just once. Now, he’s spoken to Dr. Siddhartha Mukherjee for a story in the New Yorker and actor and TV personality Joel McHale for an interview series, Joel Asks Fred Hutch. Reporters call him to comment on the preprints of papers he plans to submit for review.

Early in the pandemic, when so little was known about the new virus, but people were hungry for information about how diseases spread, Mukherjee contacted Schiffer to discuss work he’d done to model how viral dose influenced the chances of transmitting human herpesvirus 6, or HHV-6, a virus very few people have heard of.

Dr. Elizabeth Halloran, who heads the Hutch’s BBE Program, directs the Center for Inference & Dynamics of Infectious Diseases, and founded and directs the Summer Institute for Statistics and Modeling in Infectious Disease at the University of Washington, has been modeling infectious diseases since the 1980s, when she studied malaria. After 9/11, she was invited by the U.S. government and the National Institutes of Health to join modeling groups that sought to help officials prepare for the potential use of smallpox and other bioterrorist threats. This isn’t the first pandemic she’s seen that arose unexpectedly while governments and researchers focused on other risks.

As the head of an NIH-funded pandemic modeling working group, Halloran also worked on the potential threat of bird flu, only to see it suddenly superseded by H1N1 swine flu, which swept the world in 2009. Presaging the novel coronavirus pandemic, H1N1 modelers quickly switched from modeling how to contain the pandemic flu to modeling how to mitigate its damage.

Halloran has also worked on outbreaks of Ebola, Chikungunya and Zika viruses.

“We had learned a lot along the way,” Halloran said, but many modelers toiling to encapsulate human suffering in mathematical equations were feeling burnt out.

“Some of us thought, ‘We’re done. We just don’t want to see another disease.’ And then came coronavirus,” she said. “Everybody in the world suddenly felt that they know how to model infectious diseases and everybody jumped on it.”

Unfortunately, Matrajt said, this spread more than little misinformation.

Matrajt saw one model that predicted that changing when to implement social distancing measures by even a single day could change the number of deaths from COVID-19 by 50%.

“I didn’t even have to look at the model to know it was a bad model,” she said, noting that it’s mathematically impossible for a single day to make that much of a difference. “It tells me they didn’t understand the mathematics of transmission dynamics.”

An intuitive understanding of these kinds of dynamics, honed from years of experience, sometimes gave modelers insights that bordered on premonitions.

“I recall very early on hearing some people state that a vast majority of infection was from symptomatic people. Based on the wide cryptic spread of the virus, I was like, ‘No, there's no way.’ To a modeler it's extremely obvious,” Schiffer said. “Once we heard about the Biogen conference and choir practice outbreak in Skagit County, many of us had discussions where we thought, ‘OK, that’s the epidemiology. It’s aerosol.’”

From the beginning, policy makers turned to modelers for help.

Hutch biostatistician Dr. Ruth Etzioni, who has developed models to evaluate diagnostic tests for breast and prostate cancer, worked as a bridge between the Institute for Disease Modeling at the Bill & Melinda Gates Foundation and the Washington state Department of Health.

“I was thinking ahead … almost trying to be a fortune teller of what's coming: looking around, seeing what's happening in other places, what evidence are [the government] going to need from the modelers,” to support relaxing restrictions or instituting a mask mandate, said Etzioni, who leads the biostatistics core for the National Cancer Institute-funded multicenter Northwest Prostate Cancer Specialized Program of Research Excellence, or SPORE.

Drs. Betz Halloran (left), Josh Schiffer (middle) and Ruth Etzioni (right)
Drs. Betz Halloran (left), Josh Schiffer (upper right) and Ruth Etzioni (bottom right)

Photos by Robert Hood / Hutch News Service

Evolving pandemic, evolving questions

As pandemic stretched on, newbie modelers dropped out, leaving experienced modelers applying their knowledge in an environment of evolving information and evolving questions.

As a member of the World Health Organization’s epidemic response R&D Blueprint, Halloran was briefed on the emerging coronavirus on January 9, 2020. Officials wanted to know where the virus could spread. Halloran immediately reached out to Dr. Alessandro Vespignani, a collaborator at Northeastern University, to use their modeling tool, the Global Epidemic and Modeling project, or GLEAM, to project where in the world the virus could be headed as it spread from China. The team began the work before the virus received its official name, SARS-CoV-2, and submitted their first paper, which appeared in the journal Science, in late January 2020. 

Schiffer knew that the same question he’d addressed with HHV-6 — how much virus it takes to infect a new host — would be an even more important issue with SARS-CoV-2. So he, Dr. Ashish Goyal, a postdoctoral research associate in his lab, and Dr. Bryan Mayer, a BBE staff scientist with whom Schiffer had worked on HHV-6, drew on what data they could to create a similar model for the novel coronavirus.

Matrajt models how to optimize vaccine distribution — not a top priority when none exist. She initially thought her scientific involvement with SARS-CoV-2 would end with the paper that resulted from her tweet. But as vaccine developers did their best to outrace the pandemic, and candidates moved into trials at record speed, Matrajt realized she had more expertise to offer.

She’s published work in the journal Science Advances that addresses under what conditions coronavirus vaccines should be targeted at those most at risk of disease, or those most likely to spread the infection. Matrajt is currently investigating the conditions under which strategically deployed single-dose vaccines could help policy makers, faced with vaccine shortages, optimize vaccine allocation.

One of the biggest challenges to modeling the coronavirus at the beginning was the dearth of information about the unknown virus. A lot of the information that scientists studying the flu, for example, have been able to glean from past outbreaks was entirely missing.

We knew it was a coronavirus, but we didn't know how infectious is it? What’s the natural history you have to put in your models? … We had to work with a lot of uncertainty because we didn't know anything about the disease in January 2020, really,” Halloran said.

In the earliest days of the pandemic, it wasn’t even clear whether the novel coronavirus spread by jumping from human to human, as opposed to jumping to humans from its animal hosts — let alone whether contaminated objects or coughed-up mucus droplets were primary virus carriers. It would be nearly impossible for a virus that couldn’t spread between humans to spread around the world, so scientists trying to model a potentially global pandemic added the presumption of human transmission to their initial models. They also presumed that all transmission originated from symptomatic infections. Now, said Matrajt, it appears that roughly 40% of infections may be asymptomatic.  

Over time, as SARS-CoV-2 became one of the world’s most-studied viruses, scientists had to contend with a different problem: reams of data, some of it of dubious quality. 

“The availability of good data has been very hard to predict,” said Schiffer.

Prior to the pandemic, his models drew on data produced by scientists with whom he had a longstanding relationship, whose scientific standards he trusted.

“Now we are emailing people we don't know across the globe and asking for data — and getting every possible type of response you could imagine,” Schiffer said.

Even as the data that modelers could draw on changed daily, so did the world they were trying to model. Halloran and Vespignani’s first model of SARS-CoV-2 spread used transportation data to project where the virus would travel.

But by the time it got reviewed, then came all the travel restrictions. And so then we had to change the focus of the original paper — it was already outdated,” she said. They published the work in the journal Science in April 2020.

The scientific questions Halloran explored evolved with the pandemic. She and Vespignani published several studies addressing new COVID questions. They used mobility data to examine the impact of testing, contact tracing, and quarantine on the second wave of COVID-19, work that appeared in the journal Nature Human Behavior. With collaborators at the University of Florida, the team published a study in the journal Vaccine that examined the use of ensemble forecasting, a modeling strategy that uses a set of forecasts to explore a range of possible outcomes, in the design of vaccine efficacy trials.

She, Vespignani and several other colleagues also used the GLEAM model to estimate the establishment of local transmission and cryptic phase of the COVID-19 epidemic in the U.S. and Europe, and are currently looking at different targeted vaccination strategies on a global scale. Halloran also lent her expertise in the design of vaccine trials to development of the protocol for the WHO Solidarity Vaccines Trial

Schiffer also had to grapple with the pandemic’s slippery nature. He was working to figure out which variables would contribute the most to COVID-19 cases and deaths and his team’s models pointed to speed of vaccination and lockdown as the main ways society could reduce these.

“Then, of course, the news about the new variant popped up. And so we've had to re-equilibrate that whole paper,” he said.

The questions his team tackled also changed over the course of the pandemic, Schiffer said, ranging from why superspreader events were occurring to the effect masks and vaccines might have on case counts.

“It's been a very strange process to react to the news cycle,” he said.

Models aren’t a crystal ball

Many people anxiously watching the pandemic unfold expected more forecasting accuracy than the models could provide, said Etzioni. Schiffer agreed.

“Philosophically I am not in favor of using models to project what's going to happen next,” he said.

There are too many unknown variables to project a specific number of deaths within a specific time period.

“Our approach has been more to say, ‘What are the variables that will determine how many cases and deaths there will be?’ so we can go to the Department of Health and say, ‘Listen, these are the two things that matter,’” said Schiffer, who prefers to describe his models as “hypothesis generating” rather than “hypothesis validating.”

But, said Etzioni, that doesn’t mean models can’t be helpful. Early in the pandemic, many in the public struggled to understand the implications for society if the number of infected continued growing exponentially. But models could help people understand, she said.

“In a way, it didn't really matter what number the model gave to predicting how big the problem was going to be, as long as it was a big number,” Etzioni said. “The models were saying different things, but they were all saying it was going to be bad.”

In this way, models can help support policy decisions, or confirm what we know but don’t want to admit, such as that if numbers of novel coronavirus cases are climbing, we need to implement stricter social-distancing measures, she said.

At one point, Etzioni asked modelers at the IDM to do a retrospective model, comparing the numbers of infected people in Washington state to how many there might have been if lockdown measures had never been implemented.

“It really was striking, that we were was about at half of where we would have been in terms of the prevalence,” she said. The IDM model helped confirm that the difficult, unpopular restrictions had worked as intended.

Models are also often better at addressing qualitative questions, such as whether to social distance now or later, than quantitative questions, such as how many will become infected, Etzioni added.

Understanding the assumptions included in each model is key to interpreting it, the researchers said.

Modelers should be upfront about what they’ve assumed as they created their model, and how sensitive it is to those assumptions, Etzioni argued.

“We all have to tell the public the one thing that they should know that we are assuming, but that we can't really verify,” she said.

Halloran noted how much different assumptions can change the outcome of models. Take vaccines, for example. A model that assumes that vaccines prevent infection, and therefore transmission, will give dramatically different results from one that assumes that a vaccine allows breakthrough infections in vaccinated people who may then transmit the virus.

“The further you get out from the day the simulation starts, the greater the variability,” Schiffer said.

It’s a little like weather forecasting: predictions for tomorrow’s weather are much more accurate than predictions for next week. This is in part because, Schiffer noted, pandemic modelers don’t have answers to many of the parameters controlling that variability, such as how new viral variants will affect vaccine efficacy, or whether people will adhere to yet another lockdown.

“People expect big mathematical models to predict exactly what's going to happen, as if we had a crystal ball,” Matrajt said. “That’s just not possible. It would be much better if everyone, including the modelers, were a little bit more open about the limitations.”

Sabrina Richards, a staff writer at Fred Hutchinson Cancer Center, has written about scientific research and the environment for The Scientist and OnEarth Magazine. She has a PhD in immunology from the University of Washington, an MA in journalism and an advanced certificate from the Science, Health and Environmental Reporting Program at New York University. Reach her at

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