Meet the women whose work convinced the college to require vaccines

St. Olaf Magazine | Winter 2022

February 4, 2022

Meet the women whose work convinced the college to require vaccines

Mount Holyoke College Assistant Professor of Mathematics Alanna Hoyer-Leitzel '08 on the college's campus in South Hadley, Massachusetts. Photo by Rick Friedman/Polaris Images — Mount Holyoke College Assistant Professor of Mathematics Alanna Hoyer-Leitzel ’08 on the college’s campus in South Hadley, Massachusetts. Photo by Rick Friedman/Polaris Images

As St. Olaf College leaders began weighing whether to require COVID-19 vaccines last spring, consulting epidemiologist Ben Miller knew it would be important to provide data showing what the virus could look like with — and without — a highly vaccinated population on campus in the fall.

So he turned to Alanna Hoyer-Leitzel ’08 and Kate Tummers Friday ’08.

While attending St. Olaf, Hoyer-Leitzel and Friday were part of a mathematics practicum team that worked with Minneapolis VA Medical Center physician Kristin Anderson Nichol ’75 to model the impact that influenza vaccinations could have on a college campus. They published a paper on their findings that, more than a decade later, caught Miller’s attention.

“A lot of the work they had done was immediately applicable to the questions we were trying to answer about requiring the COVID-19 vaccine,” Miller says.

Both Hoyer-Leitzel and Friday had gone on to careers directly linked to the work they had started at St. Olaf. Hoyer-Leitzel is an assistant professor of mathematics at Mount Holyoke College in Massachusetts whose research focuses on dynamical systems. Friday is a partner at TigerRisk Partners, where she spent years specializing in catastrophe modeling and analytics.

Kate Tummers Friday '08 at her home office in Minneapolis. Photo by Steven Garcia '20 — Kate Tummers Friday ’08 at her home office in Minneapolis. Photo by Steven Garcia ’20

Miller reached out to the two alumni, and together the trio developed a mathematical model to show the impact of different rates of COVID-19 vaccination on a college campus with 3,000 students.

The COVID-19 vaccination model was much more sophisticated than the one Hoyer-Leitzel and Friday had developed as students, but its key takeaway was simple: a very high percentage of the campus community would need to be vaccinated in order to prevent large outbreaks of the virus. This would be especially true as more contagious variants of COVID-19 emerged.

College leaders were convinced. On June 15, St. Olaf became one of the first colleges in Minnesota to announce that it would require all students, faculty, and staff to be fully vaccinated against COVID-19 before the start of the fall semester.

“Requiring vaccines is the most safe and effective line of defense against COVID-19,” President David R. Anderson ’74 wrote to the campus community.

By the fall, many colleges and universities across the country had reached the same conclusion.

“This modeling work was central to our early move to require vaccines,” says Vice President for Advancement Enoch Blazis, who leads the college’s COVID-19 response efforts. “And in spite of the challenges of the Delta and Omicron variants, it has been essential in keeping us ahead of the curve instead of behind it.”

This modeling work was central to our early move to require vaccines. And in spite of the challenges of the Delta and Omicron variants, it has been essential in keeping us ahead of the curve instead of behind it.Campus COVID-19 Response Lead Enoch Blazis

Following the data
Hoyer-Leitzel led the team’s efforts to model the impact of various levels of COVID-19 vaccination on campus. To do so, she used an epidemiological tool called an SIR model that examines how an infectious disease will move through a population of people who are susceptible (S), infected (I), and recovered (R).

The model would be simple, Hoyer-Leitzel says, if you could assume that the vaccine is 100% effective and that people who are vaccinated or recovered are no longer susceptible to the virus. But as most of us now know from this pandemic, that is not how the science of infectious diseases works.

"The simplest standard model for an epidemic is called an SIR model, where SIR is an acronym for the three population subgroups of susceptible (S), infectious (I), and recovered (R). The population starts mostly in the susceptible group with a few individuals in the infectious group. As susceptible and infectious people interact, the number of infectious individuals grows, until a certain threshold is reached where the rate of new infectious individuals starts to decrease. Infectious individuals recover at a certain rate, based on the average length of infection. For the St. Olaf model, we included two additional population subgroups — susceptible vaccinated individuals (Sv) and infectious vaccinated individuals (Iv) — to allow for different contagion and recovery parameters between vaccinated and unvaccinated populations. Above is a schematic showing the path of individuals through the population subgroups. The model assumes no other mitigation measures besides the vaccine: no masking, no testing, no isolation for infectious individuals," Alanna Hoyer-Leitzel '08 says. — “The simplest standard model for an epidemic is called an SIR model, where SIR is an acronym for the three population subgroups of susceptible (S), infectious (I), and recovered (R). The population starts mostly in the susceptible group, with a few individuals in the infectious group. As susceptible and infectious people interact, the number of infectious individuals grows, until a certain threshold is reached where the rate of new infectious individuals starts to decrease. Infectious individuals recover at a certain rate, based on the average length of infection. For the St. Olaf model, we included two additional population subgroups — susceptible vaccinated individuals (Sv) and infectious vaccinated individuals (Iv) — to allow for different contagion and recovery parameters between vaccinated and unvaccinated populations. Above is a schematic showing the path of individuals through the population subgroups. The model assumes no other mitigation measures besides the vaccine: no masking, no testing, no isolation for infectious individuals,” Alanna Hoyer-Leitzel ’08 says.

Adding to the complexity is the fact that vaccine efficacy often wanes over time, and emerging variants of the virus have the potential to be more contagious. Both of those factors proved to be especially true with COVID-19. The highly contagious Delta variant began emerging while Hoyer-Leitzel was building her SIR model, as did evidence showing that the vaccine’s protection began waning after six months. Her work had to take all of this into account.

“So you end up creating more differential equations and getting a more complicated model,” she says.

Hoyer-Leitzel notes that the model doesn’t take into account other mitigation measures like masking, testing, or physical distancing. And although the team tried to assume a “worst-case scenario” for how contagious the disease might become, the Delta and Omicron variants have far exceeded those predictions.

For those reasons, Hoyer-Leitzel says, the goal of the model isn’t to accurately predict the number of COVID-19 cases on campus in a given week or semester. Its goal is to show how certain levels of vaccination can stem the number of cases. For that, the model was clear: having a vaccination rate well above 90% would be key to preventing large outbreaks on a small campus with densely populated housing.

“It was just eye-opening to see that once you hit a certain threshold of vaccination, the total number of people infected becomes very small,” Friday says. “The model was able to test different assumptions with vaccine efficacy and infectious rates and in all scenarios, it was clear that a high rate of vaccination would have a very positive impact on reducing the spread of COVID-19.”

Alanna Hoyer-Leitzel ’08 says: “The schematic from the SIR figure above was translated into a set of five differential equations, meaning we infer a relationship about the rate at which the population in each subgroup is changing. St. Olaf consulting epidemiologist Ben Miller provided expertise on the parameters of the model — for example, how infectious individuals would be and for how long. We then solve the system of differential equations using numerical techniques and find the cumulative cases at the end of one semester for different vaccination rates and different vaccine effectiveness. With lower vaccination effectiveness, it takes a much higher vaccine rate to control the spread of a disease.”

“One of the difficulties in modeling COVID-19 outbreaks is the unknowns, specifically how contagious COVID-19 is and the effectiveness of our vaccines. Both of these change with new variants,” Alanna Hoyer-Leitzel ’08 says. “Our model (as well as models by other COVID researchers) gives a threshold at which the rate of new infections will be negative (i.e., the number of new infections is decreasing) given by the equation (1-ϵV) R0≤1, where ϵ is the efficacy of the vaccine, V is the fraction of people vaccinated, and R0 (R-naught) is a measure of how contagious the disease is. In this figure, we plot the ‘safe zones’ (shaded regions) for various values of R0 where the number of new infections should be expected to decrease. For example, for R0=2, the number of new infections should be expected to decrease in the green shaded area. If we assume the vaccine is 70% effective, corresponding to a horizontal value of 0.7, we would need the vaccinated fraction of the population to be greater than 0.714 (or 71.4%) to expect the number of new infections to decrease. Also note how small the ‘safe zone’ becomes when R0=6 (the Delta variant has an R0 of 6.4). Knowing that our current vaccines are not greater than 80% effective, we need 100% vaccination to control the spread of new cases as well as additional mitigation measures such as mask wearing, social distancing, and surveillance testing. These mitigation measures become even more important with the Omicron variant, which has an R0 of 10-12. For the graph earlier in the story, the team assumed an R0 of 4.”

Alanna Hoyer-Leitzel ’08: “When R0 or the value of (1-ϵV) R0 are close to one, this means that one sick person infects approximately one more person. This leads to outbreaks with low current case counts that linger in the population for a while and it is hard to predict how long an outbreak could last. It could die off quickly if a sick person ‘fails’ to infect someone else or it could last a long time. Because the differential equations model uses a continuous fraction of the population, it can give good long-term results, but there will be fractions of new cases each day, which is not realistic. For comparison, we used a probabilistic continuous time discrete population Markov chain model. Because it is probabilistic, each computer simulation of this model is different, so we look at the mean and standard deviation of 1,000 probabilistic simulations. Above is a graph containing the cumulative cases for probabilistic simulations (colored curves), the mean cumulative cases (dashed curve), and the ODE deterministic cumulative cases (solid curve). In this case, the deterministic prediction is 286 cumulative cases at 150 days, while the mean of the probabilistic simulations is 270 cases. However, the probabilistic simulations have a standard deviation of 223 (50% of simulations have cumulative cases in the range of 47-493). Out of 1,000 simulations, 459 naturally die off (0 infected people at some point before t=150) in a mean of 61.5 days. Here we’re using 70% effective vaccine with 75% vaccination rates and R0=4 so that (1-ϵV) R0=(1-0.7*0.75)(4)=1.9.”

Having served as the college’s health consultant since the early days of the pandemic, Miller — the vice president of public health and regulatory affairs with The Acheson Group — knew college leaders would follow the science. He had advised the college on COVID-19 testing and contact tracing, and worked with college staff to develop protocols for room usage based on airflow and HVAC measurements. These mitigation measures had enabled St. Olaf to have in-person, on-campus classes throughout most of the pandemic. By adding vaccines, the college would be able to resume many extracurricular activities throughout the fall semester.

“Having St. Olaf put its weight behind science that really says these vaccines are safe and effective is one of the things that made a significant difference,” Miller says.

Having St. Olaf put its weight behind science that really says these vaccines are safe and effective is one of the things that made a significant difference.Consulting Epidemiologist Ben Miller

This same data-driven approach led the college to also require booster shots. All St. Olaf students, faculty, and staff were required to receive a booster dose of the COVID-19 vaccine by February 1.

“It is essential to look at the numbers because that creates a realistic view of the possible challenges of the pandemic and the effect of mitigation measures versus guessing,” Blazis says. “By using this modeling and looking at other studies, it was apparent that a vaccinated campus would be safer for our congregate setting and allow for more of the campus experience.”

Ben Miller, the vice president of public health and regulatory affairs with The Acheson Group, at his home office in Northfield. Photo by Evan Pak '19 — Ben Miller, the vice president of public health and regulatory affairs with The Acheson Group, at his home office in Northfield. Photo by Evan Pak ’19

Mathematical minds
Having alumni with the expertise to model the potential power of vaccines was a game changer.

Hoyer-Leitzel and Friday are both graduates of St. Olaf’s nationally recognized mathematics program, which focuses on innovative teaching and learning. As students they participated in a mathematics practicum led by Professor of Mathematics, Statistics, and Computer Science Steve McKelvey that pairs teams of St. Olaf students with organizations to address real-world issues. Their team — which also included Matt Moynihan ’07 and Jennifer Marsh Rhudy ’07 — worked alongside Nichol, a Minneapolis Veterans Affairs Health Care System administrator whose research has focused on issues relating to adult vaccines, with a special emphasis on influenza and pneumococcal vaccination.

“She wanted to know what the effect would be of vaccinating for the flu on college campuses,” Hoyer-Leitzel says.

The team developed an SIR Model to examine the impact. Following the practicum, Friday continued working with Nichol and McKelvey to prepare their findings for publication.

“I really like to see how mathematical models impact real life, how they can inform these big, important decisions,” Friday says.

Kate Tummers Friday ’08I really like to see how mathematical models impact real life, how they can inform these big, important decisions.

That eventually led Friday to pursue a career in catastrophe risk consulting and reinsurance, working for companies that include Collins, Guy Carpenter, and TigerRisk Partners.

Kate Tummers Friday '08 outside her home in Minneapolis. Photo by Steven Garcia ’20 — Kate Tummers Friday ’08 outside her home in Minneapolis. Photo by Steven Garcia ’20

Hoyer-Leitzel continued to pursue her love of math in graduate school, earning a Ph.D. in mathematics. When she decided to teach, she knew she wanted to be at a liberal arts college where she could mentor students in the same way her professors at St. Olaf had done.

“What St. Olaf really did to prepare me for where I am now is instill in me this idea that anyone who wants to study math can,” Hoyer-Leitzel says. “It’s not about ‘the best and the brightest.’ Everyone can do this. That’s something I took with me, something I still believe, and something I now teach my own students.”

Alanna Hoyer-Leitzel ’08What St. Olaf really did to prepare me for where I am now is instill in me this idea that anyone who wants to study math can. It’s not about ‘the best and the brightest.’ Everyone can do this. That’s something I took with me, something I still believe, and something I now teach my own students.

Hoyer-Leitzel’s research at Mount Holyoke, which often includes her students, focuses on applications of dynamical systems. “I like to think that the field steals the tools from every other area of mathematics that it needs to be able to solve the problems that we have,” she says.

Assistant Professor of Mathematics Alanna Hoyer-Leitzel '08 in her office at Mount Holyoke College. Photo by Rick Friedman/Polaris Images — Assistant Professor of Mathematics Alanna Hoyer-Leitzel ’08 in her office at Mount Holyoke College. Photo by Rick Friedman/Polaris Images

Some of her recent work has examined how mathematicians might model resilience using a dynamical system. She’s used these modeling techniques to examine how resilient a savanna ecosystem is to different types of fire. She’s in the early stages of applying the same modeling framework to the human immune system. Hoyer-Leitzel says it could help answer the question “How resilient are we to repeated viral exposure?” and could be applied to everything from the common cold to COVID-19 to ebola.

“I’m excited to build that work up,” she says.

In the meantime, her work has already had a meaningful impact at St. Olaf.

“It was really exciting to be able to work with alumni who were so well-positioned to step in and be able to do this modeling work in a short amount of time,” Miller says. “I think it’s a testament to St. Olaf that you have alumni who are not only well-educated and have this expertise, but are also so willing to step up during this busy time, roll up their sleeves, and help out their alma mater.”