Fourth Virtual Dean's Workshop Highlights Mathematical Modeling as a Valuable COVID-19 Tool

The COVID-19 pandemic has familiarized every news watcher with graphic curves that represent the number of infections over time. For policymakers, those curves served as flashlights amid the murk of the early pandemic, and they continue to guide decision-making. All of them depend on sophisticated mathematical modeling and quantitative science, the topics of the fourth virtual Dean’s Workshop on the pandemic, held May 21, 2020.

“During both the local acceleration of the pandemic and today as we experience a decline in the number of cases and strive to reopen safely, we have relied heavily on our modeling,” said Nancy J. Brown, MD, the Jean and David W. Wallace Dean of Medicine and C.N.H. Long Professor of Internal Medicine.

In normal times, university scholars go where their curiosity takes them. But during a pandemic, consequences should guide decisions, said Saad B. Omer, MBBS, MPH, PhD, director, Yale Institute for Global Health: “You start with a question and work backward.”

Omer took viewers through a series of questions that have led him to collaborative research across Yale and beyond. How, for example, do social-distancing guidelines affect mobility? With Eli P. Fenichel, PhD, Knobloch Family Professor of Natural Resource Economics at Yale School of Forestry & Environmental Studies, Omer used cellphone data to learn that, while social-distancing mandates were followed by a dramatic decrease in people’s mobility, many had begun to voluntarily reduce their movements even before the mandates were issued. That suggests that people may not revert to pre-pandemic habits once restrictions lift, his team concluded.

Are there better ways to monitor community transmission? With collaborators that include the World Bank as well as Edward H. Kaplan, PhD, William N. and Marie A. Beach Professor of Operations Research, and professor of public health and of engineering, and Jordan Peccia, PhD, Thomas E. Golden, Jr. Professor of Chemical & Environmental Engineering, Omer has found that sampling sewage sludge can give a snapshot of the outbreak days before COVID-19 hospital admissions can.

To track infectious-disease transmission, epidemiologists use two measures: R-naught (or R₀)—the average number of secondary infections that a primary case produces in a susceptible population—and the more complex R_t, which takes immunity and control efforts into account. Both measures make an unwarranted assumption, though, said Virginia Pitzer, ScD, associate professor of epidemiology (microbial diseases), they assume that the fraction of undetected cases is about the same over time. That is not true in the case of COVID-19, she said: “There has been a lot of variation in testing effort and reporting fractions through time.” So Pitzer and her team developed mathematical tools to tease apart whether observed increases in the number of cases reflects an increase in testing capacity (such as a new lab offering testing), a broadening of testing criteria (such as allowing non-healthcare workers or asymptomatic people to be tested), or a true rise in infections. That, in turn, allows for better estimates of R_t, which helps policymakers more accurately weigh how effective interventions have been.

The United States’ COVID-19 death count has become a “radioactively hot topic,” said Daniel Weinberger, PhD, associate professor of epidemiology (microbial diseases). In partnership with federal agencies and other universities, his group is crunching publicly available data on recent deaths of U.S. residents, trying to understand how many are related to the pandemic. Deaths blamed on pneumonia and influenza (P&I) could, for example, conceal actual COVID-19 deaths, particularly in places where testing has been slow to ramp up. The researchers compared all-cause- and P&I-related deaths this year to what would be expected based on previous years. This macabre arithmetic has revealed roughly 80,000 excess U.S. deaths, regardless of cause, in March and April of 2020. That puts the estimated pandemic-related toll about 50% higher than the reported numbers of COVID-deaths. “We have good reason to think the number of reported (COVID-19) deaths is an undercount,” Weinberger said.

Early in the course of the coronavirus pandemic, a disproportionate number of celebrities, including Boris Johnson and Tom Hanks, were testing positive. Part of that may reflect their privileged access to testing, said Nicholas A. Christakis, MD, PhD, MPH, Sterling Professor of Social and Natural Science. But those people’s social connectedness also played a role, boosting their vulnerability to infection above that of others who move in more limited social circles. “They’re more connected, so they get stricken earlier,” Christakis said.

In a new downloadable app powered by a machine-learning algorithm, Christakis is using that phenomenon to identify and track illness among well-connected people—“canaries in the coal mine” whose infections signal that a new outbreak is beginning to emerge in their communities. Called Hunala, the app combines daily symptom check-ins with information about users’ location and social interactions. A disproportionate rise in symptoms among more socially connected, higher-risk people is “a harbinger that the epidemic is going to spike,” Christakis said.

Another early warning could come from medical notes in the electronic health record (EHR). Julie Womack, PhD, CNM, FNP (BC), associate professor of nursing, is working to adapt an algorithm that can read providers’ notes about a patient’s medical visit from the Veterans Health Affairs EHR. Womack’s team is training this algorithm, which combines natural-language processing and machine learning, to recognize a variety of descriptors that could signal COVID-19, such as “fever” or “cough” or “can’t smell.” Her team will test the “system extractor pipeline” on the records of thousands of veterans who have tested positive for COVID-19. If it spots COVID-19 symptoms reliably, Womack plans to use the tool to study questions like which symptoms are the most emblematic of COVID-19 and which reflect a higher viral load, as well as to develop surveillance systems to spot new surges.

“Help. We Matter 2,” read a sign placed in a window at Chicago’s Cook County Jail, which in early April was the site of an especially severe COVID-19 outbreak. “Correctional facilities present an ideal setting for infections to spread,” said Emily Wang, MD, MA, associate professor of medicine (general medicine); and co-director, Center for Research Engagement, Internal Medicine. People frequently enter and leave the crowded facilities, which typically lack basic sanitation tools and adequate medical care. Wang is part of a coast-to-coast team building a model of COVID-19 transmission in correctional facilities. The goal: to compare mitigation techniques and determine which ones are most effective, as well as build a tool to help correctional system leaders make decisions to better protect people with chronic health conditions.

So far, they are learning that asymptomatic testing and placing people in single cells are associated with decreasing the transmission rate. Large-scale releases also appear to drive down infection rates within facilities. However, release can then increase health risks beyond prison walls. Even without a pandemic, formerly incarcerated people—disproportionately people of color, Wang noted—experience high rates of hospitalizations and deaths immediately after release, especially those without adequate housing or social support.

Transitions Clinic, which provides primary care to formerly incarcerated Connecticut residents, has adapted with such innovations as providing buprenorphine via telehealth; meeting patients on the New Haven Green; and creating a COVID-19 state hotline for halfway houses and parole officials to create lower-risk medical discharge plans. Wang offered ways the public can help ease the crisis for people who are incarcerated.

Connecticut’s COVID-19 outbreak is dwindling, and on May 20, the state of Connecticut began to reopen. It will be a gradual process. To support Governor Ned Lamont’s expert advisory panel, Forrest W. Crawford, PhD, associate professor of biostatistics, of ecology and evolutionary biology, of management, and of statistics and data science, was asked to use state-specific data to calculate how Connecticut’s outbreak might behave under various reopening scenarios. “Model projections that my group has been developing have the ability to tell us about possible futures,” he said.

Those futures vary dramatically based on how quickly reopening proceeds. Under a slow-reopening scenario, in which 10% of latent suppressed social contact is released each month, new infections and hospitalizations will rise in late summer, but at a rate well below Connecticut hospitals’ capacity. The total number of deaths under this optimistic projection: 4,600 to 7,100 by September 1.

By contrast, if reopening proceeds faster, with 10% of suppressed contact released every 2 weeks, the death toll could reach 5,400 to 13,400 by September 1, with hospitalizations jumping in late July and hospital capacity disastrously exceeded by late August.

Most likely, Crawford said, Connecticut will experience an intermediate scenario. The team will post an updated projection report here each month.

Since early March, Kaplan has been a member of Yale’s in-house team of advisors, helping the university’s leaders with decisions about social distancing and testing by building what he calls “scratch models”—those created quickly and in real time. Kaplan is now creating scratch models of the value of repeatedly screening campus residents for infection (as opposed to testing only health care workers, or only symptomatic people).

His models suggest that if everyone is tested weekly with a test that is 70% effective at picking up cases, we could potentially block about 58% of transmission days by isolating people who test positive.

More complex analyses demonstrate the power of frequent testing and isolation even more clearly. If students return to campus in the fall with moderately effective social distancing, but no screening, 20% are infected by Thanksgiving. By contrast, screening every 2 weeks yields a 3.5% infection rate, and weekly screening 1.5%.

With ineffective social distancing and no screening while infections are unknowingly acquired off campus, the vast majority of people contract the virus by Thanksgiving. With screening every two weeks: nearly half are infected. With weekly screening: 4%.

“The logistics [of frequent testing] can easily become overwhelming, but nonetheless it’s a very important activity if the idea is to try and really curtail the spread of infection,” Kaplan said.