As governors across the country reopen their states’ economies, policymakers are relying on disease models for help in predicting where new coronavirus cases may surge as stay-at-home orders expire.
“The math is unfortunately pretty simple,” said Jeffrey Shaman, a leading epidemiologist at Columbia University. “It’s not a matter of whether infections will increase but by how much.”
To answer that question — by how much? — epidemiologists like Shaman use computer models to project a range of possible futures based on assumptions about the nature of the disease and how society will react to it.
Projections from different teams, such as those by the Institute for Health Metrics and Evaluation at the University of Washington and Shaman’s group at Columbia, often are in disagreement. That leads some people to question the usefulness of models: They can’t all be right, so perhaps they are all wrong.
Yet such disagreements are inevitable, and they render disease models more, rather than less, useful. To understand why, one must grapple with the deep uncertainty at the heart of the practice of disease modeling.
Imagine you are an epidemiologist, and one day the governor sends you an email about an emerging new disease that has just arrived in your state. To avoid the complexities of a real disease like covid-19, the illness caused by the novel coronavirus, we have created a fake disease called Simulitis. In the article below, we’ll give you the chance to model some scenarios — and see what epidemiologists are up against as they race to understand a new contagion.
I’ve been reading reports about this new respiratory disease, Simulitis. It seems to be spreading from country to country pretty quickly. I’m worried that we might not be prepared for a wave of infections if and when it finally arrives here.
My aides tell me you’re the best disease modeler in the business. Can you tell me how many cases we can expect here?
Having closely followed reports of the contagion as it spreads across the world, killing thousands and overwhelming hospital systems, you have been expecting an email like this one. You want to come through for the governor, but this is a new disease, and much of the information you would need to create a basic model to project its spread remains unknown.
To build even the crudest model, you need to estimate the basic reproduction number, what epidemiologists like you refer to as R0, or “R naught.” That’s scientific shorthand for the average number of people each sick person infects at the beginning of the outbreak, before anyone has become immune.
You open your computer and begin looking for published studies that estimate the R0 of Simulitis. You find two; they are not in agreement. That’s a start.
To update your model, click a study in the panel on the left and watch the chart update on the . Be sure to click both studies to compare their outputs.
You are researching R0.
That’s the average number of people each contagious person infects.
Since the virus does not behave identically in each person it infects — for example, some people will remain contagious longer than others — the model introduces randomness to account for that uncertainty. That is why you see that tangle of lines, some steeper and others flatter, representing a range of possible outcomes.
Additional uncertainty comes from the different values for R0. The article from Science University, which estimates an R0 of 5, is based on research into an outbreak in the Middle East, while the estimate of 3.5 from the Ministry of Disease Control is based on an outbreak in South America. Which report is more trustworthy? Hard to know at this early stage of the novel disease.
What is certain: The model’s output is highly sensitive to a changing R0. If the Science University article is right, the outbreak should peak in about 50 days, with over 15 percent of your state’s population infected. If the Ministry’s estimate is right, the peak will come in about 75 days, and fewer people will be sick when the peak hits.
The real-life epidemiologists racing to figure out the coronavirus will tell you that dealing with uncertainty is the core of a disease modeler’s work.
“One of the most notable features of emerging pathogens is that early information is very unstable,” said Natalie Dean, a biostatistician at the University of Florida who specializes in infectious disease epidemiology. “People don’t understand how uncertain the numbers are.”
“Every input was uncertain,” said Corey Chivers of his team’s early covid-19 models. He is the lead data scientist for Penn Medicine’s Predictive Healthcare Team, whose models are in use by hospital systems across the country. “We were trying to give bounded scenarios. So, to say, let’s be pessimistic about all these parameters and give you a projection, let’s be optimistic about all them and give you a protection, and suggest maybe it’s somewhere in between.”
As you try to model the spread of Simulitis, your job is to be forecaster, not fortune teller, and project a range of possible outcomes based on different assumptions.
Two weeks later in your imaginary life as an epidemiologist, an email arrives from the hospital director.
Patients sick from Simulitis have begun to show up at the hospital. I’m concerned we’re going to run out of beds.
Can you make a model to forecast whether our hospital will be overrun?
The Hospital Director
By now, your state’s health department has recorded two weeks of increasing cases. The data tentatively suggest an R0 of about 5, which you can build into your model.
In addition to the R0, there are two more basic numbers you could use to make your projection for the hospital director. First, you need to estimate the hospitalization rate — that is, the share of infected people so sick they go to the hospital.
Second, you can research the infectious period — the average number of days a sick person remains contagious. You choose to use that as a proxy for how long those sick enough to be hospitalized will remain there.
You open your computer and find studies estimating both of these numbers.
You are researching the hospitalization rate and the infectious period.
These two variables interact to affect the number of hospitalizations.
What do you tell the director? On the one hand, if the optimistic estimates — a 20 percent hospitalization rate and three days of infectiousness, on average — prove accurate, the hospital should have sufficient beds. If, however, the more dire possibilities develop, the hospital will be completely overwhelmed with sick patients in a matter of weeks.
As you did for the governor, you present the full range of possible outcomes and emphasize that Simulitis looks worse than other infectious diseases you have studied. You advise the director that it would be better to prepare for a catastrophe that never happens than be overwhelmed by an unexpected flood of patients, even if finger-pointers later call you an alarmist.
Here’s Dean again. “I can’t tell you how many times I’ve been called a fearmonger,” she said. “But the reality is … I remember being very clear that there was virtually no risk of Ebola spreading in the U.S.”
With the coronavirus, she began sounding the alarm early, after surveillance of cases in China that emerged before Jan. 26, and “people like to accuse me of overhyping,” she said. “But it’s very serious.”
Two weeks after your forecast for the director, the Simulitis epidemic has killed thousands of people in your state. Desperate to slow the spread and save lives, the governor emails you again.
Simulitis is out of control. People are dying. What can I do to slow this thing down?
Your earlier disease models have prepared you to try to answer this urgent question. And you’ve gathered new information about this pathogen as it spreads, which allows you to tweak your model to forecast how case counts might change based on different scenarios.
Infectious-disease experts spend a lot of their time assessing how human behavior affects the spread of deadly viruses. One of the important variables in modeling contagion is the contact rate, meaning how many people each person interacts with each day.
“You can say, well, now [that] we’ve put together a model of how this disease works, what happens if a bunch of these people who are susceptible, you make them all stay in their homes so they’re not going to have contact?” explained Helen Jenkins, an assistant professor of biostatistics at the Boston University School of Public Health.
You open your computer and run some simulations to show the governor how enforced social distancing could lower the contact rate and slow the spread of infections.
You are researching .
Reducing the contact rate will slow the spread of infections.
If people continue to behave as if nothing out of the ordinary is happening, cases will continue to climb rapidly.
If, however, the governor orders nonessential businesses to close, that will reduce the opportunities for people to interact, lowering the contact rate. You cannot be sure by how much, but you estimate it could cut it in half.
If the governor also issues a stay-at-home order, that will slash the contact rate even further, perhaps to one-fifth of normal levels.
Social distancing will slow the disease while causing economic upheaval. Your responsibility as a public health specialist is to present the range of possible outcomes. It is now the governor’s challenge to weigh the human lives that will be lost without social distancing against the suffering that will be caused if the measures are enforced.
Your social distancing projections encouraged the governor to shut down most businesses and issue a stay-at-home directive for the state’s residents. Within weeks, new numbers have spiked: unemployment numbers.
The stay-at-home orders seem to have worked. Eight weeks after the first case, the spread of Simulitis infections has slowed.
With new Simulitis cases declining, you get another email from the governor.
Your projections convinced me we needed to shut down the economy. But our citizens need to get back to work. When can we reopen?
There’s still no Simulitis vaccine, and no way to measure immunity, so if the governor eases social distancing rules, an uptick in cases will occur. You sit at your computer and run some simulations to find out what would happen if Simulitis starts spreading as fast as it did before.
You are researching when to reopen the economy.
Reopening could cause a second wave of infections.
It is clear that reopening the economy could result in a significant second wave of cases. As your model shows, the purpose of the governor’s social distancing policy was not to eradicate the disease, but to buy time to scale up testing and contact tracing, which would make it possible to identify new cases and isolate those infected before new local outbreaks could emerge.
But opening before that could be perilous, as the real-life epidemiologists who are working to guide policy on the coronavirus have repeatedly warned.
“Unless we have those systems in place to actually track down these cases and prevent them from spreading further, it’s just going to take back off,” Dean said. “I don’t know that people really understand the scale of the effort that’s going to need to go in.”
Chris Alcantara contributed to this story. Editing by Ann Gerhart and Monica Ulmanu.
This article uses an SEIR model adapted from code written by Dr. S. Scott Collis, the Director of Computing Research at Sandia National Laboratories and a former faculty at Rice University. The code represents Dr. Collis’ own work and is not affiliated with his present or prior employers. The implementation is itself based on a paper published in March, 2020, by Yao Yu Yeo, Yao-Rui Yeo, and Wan-Jin Yeo.
The scenarios for the Simulitis models were constructed by the authors but were based on advice from Dr. Corey Chivers, Lead Data Scientist for Penn Medicine’s Predictive Healthcare Team; Dr. Natalie Dean, Assistant Professor of Biostatistics at the University of Florida College of Public Health & Health Professions; Dr. Helen Jenkins, Assistant Professor of Biostatistics at the Boston University School of Public Heatlh; Dr. Jeffrey Shaman, Professor of Environmental Health Sciences and Director, Climate and Health Program, at Columbia University; and Dr. Theo Vos, Professor of Health Metrics Sciences at the Institute for Health Metrics and Evaluation at the University of Washington.