This article was originally published in the AIMatters newsletter and written by Estelle Basor.
Over forty graduate students and advanced undergraduates participated in an online summer program to study dynamics and data in the COVID-19 pandemic. The program was sponsored by AIM and the NSF.
Students had the opportunity to learn the basic mathematical epidemiology underlying the models used in studying COVID-19 using a dynamical systems perspective. The first three weeks of the program were focused on getting the students up to speed on the mathematics of the modeling. During the first week, possible research questions were identified. The second week was devoted to understanding the models better, and the third-week emphasis was on data. The faculty leaders designed many interesting activities to help students get ready for the actual research. For example, in Week One, an afternoon was devoted to a role-playing session where two students played the role of policymakers and another two acted as scientists.
To help structure the activities and give a sense of belonging, the summer school used a virtual office space called Sococo. An image is provided so the reader can see the layout. Each participant had an office. There were meeting rooms, an “all hands on deck” room, a library, a kitchen, and even a cafe. Often everyone would meet in the “all hands” room, and then break up into smaller groups that worked in a meeting room or an individual office. Sococo allows one to start a Zoom meeting in a room, write together on a whiteboard, post links to materials, chat, watch a movie, or have a session of tai chi together.
The fundamental model of epidemiology is called the SIR model. The population of interest is subdivided in three groups, or compartments, of individuals: Susceptibles (S), Infected (I), and Recovered (R); each
individual is in some compartment. An epidemic is then thought of as a flow through the compartments, from S to I to R. There are variations of the SIR model, as well as other models that involve stochastic approaches, network approaches, and agent-based models, where the behavior of each individual separately is taken into account.
The students were guided by ten faculty from universities around the country: John Gemmer (Wake Forest), Sarah Iams (Harvard), Hans Kaper (Georgetown), Richard McGehee (Minnesota), Nancy Rodriguez (CU-Boulder), Steve Schecter (NC State), Mary Silber (Chicago), Erik Van Vleck (Kansas), Mary Lou Zeeman (Bowdoin), and the program director, Christopher Jones (UNC-Chapel Hill). They were supported by five mentors, who are junior faculty, postdocs, or advanced graduate students: James Broda (Bowdoin), Punit Gandhi (Virginia Commonwealth), Kaitlyn Martinez (Colorado Mines), Christian Sampson (UNC-Chapel Hill), and Maria Sanchez- Muñiz (Minnesota). Critical to the effort was a panel of experts, most of whom are mathematical epidemiologists, but also included a statistician, a medical expert, and two health industry researchers: Linda Allen (Texas Tech), Pauline van den Driessche (UVic), Nicholas Ma (Cerner), Cordelia McGehee (Mayo Clinic), Andrew Roberts (Cerner), Jianhong Wu (YorkU), and Abdul-Aziz Yakubu (Howard).
After the initial three weeks of listening to lectures, videos and multiple discussions, the research was divided into five overarching areas. Students then formed into groups studying smaller subtopics.
To find and read the full article and past issues of AIMatters, visit https://aimath.org/aimnews/newsletter/.
Summer School Student Spotlight
Forty-one advanced undergraduates and graduate students participated in the AIM Summer School. They were chosen from over 550 applicants and they were a motivated, dynamic, and hard-working group of students. One of the students was Tayler Fernandes Nunez, whom we interviewed at the end of the school.
Tayler was a member of the five-person Age-structured Population research group, which studied the question of how COVID-19 spreads between two populations based on age range. Her research group focused on the population of the state of Illinois, which was chosen based on both the diversity of its inhabitants and the availability and reliability of COVID-19 case-related, age mixing, and overall mobility data.
We asked Tayler her thoughts on the Summer School and working in a virtual world. She said the work was both exciting and exhausting, but that she especially liked the freedom to be able to ask lots of questions of her fellow researchers to sort out the issues that came up. She enjoyed the online tai chi
sessions and the mentorship of the leaders. Taylor also remarked that the team developed a strong friendship in their six weeks of work. Their team name was “Best Friends Club.”
We also asked her thoughts about the virtual office space, Sococo, which provides a sort of blue print of an office space with lecture halls, meeting rooms and offices. Tayler replied that it provided structure and allowed for a mental transition when switching tasks.
Tayler had the opportunity last year to attend a Research Experience for Undergraduates (REU) program that had a pure mathematics emphasis. The summer school with the focus on modeling aspects of a pandemic was quite the opposite. She said that she really enjoyed “being grounded in the applied mathematics” and may pursue that direction in graduate school.
Tayler received her undergraduate degree in mathematics from Northeastern University this past May. This fall she will attend the Postbaccalaureate program at Smith College and will then enter a PhD program the following year.
Summer School Project Spotlight
The summer school projects were divided into five overarching areas and then each subdivided into smaller topics. These ranged from examining the set up of testing sites, to the study of the uninsured in the spread of the pandemic, to the role of air quality as a factor in the spread of COVID-19. Here is a highlight of one of the projects that investigates the effects of university scheduling on the surrounding community, a topic that is of much current interest.
How would changing the class schedule of university students affect the spread of COVID-19 in the surrounding community? This is the kind of question considered by Elijah Pivo, Colin Roberts, and Claire Valva. For example, if half of the students attend in-person classes one week, and then go online the following week, while the other half of the students do the opposite, will it help reduce the number of infected individuals in the surrounding community? Or what happens if students are only in class with students of the same major, thereby reducing the number of contacts? These are important and timely questions as universities and schools try to navigate the reopening of their institutions and have concerns about the effect on the cities where the universities are located.
Given the complexity of disease spread, as well as the growing availability of data, the team proposed a multi-scale framework, in conjunction with data assimilation techniques, to investigate the viral spread of COVID-19. The multi-scale framework was a combination of agent-based modeling, where each person is modeled individually, combined with an approach where individuals are compartmentalized.
For example, using Fort Collins, Colorado, and Colorado State University, they derived the contact rate within the university from the agent-based model, and the contact rate within the greater city from parameter estimation from current Fort Collins COVID-19 infection rates.
Their preliminary results, among a variety of interesting findings, predicted that increasing the number of in-person classes (periods) attended each day increases the contact rate in a linear fashion, and that staggered schedules did indeed “flatten the curve” for the surrounding city.
These techniques can be applied to many other situations including workplaces and K-12 classrooms. The group plans to improve their models, publish their results, and then make the work available to others.
Elijah Pivo received his undergraduate degree from Johns Hopkins University in Electrical and Computer Engineering and is beginning a PhD program at the MIT Institute for Data, Systems and Society.
Colin Roberts is a fourth-year PhD student at Colorado State University, where he also received his undergraduate degree in Mathematics and Physics.
Claire Valva received her undergraduate degree from the University of Chicago majoring in Geophysical Sciences and Mathematics and is entering the PhD program at the Center for Atmosphere Ocean Science at the Courant Institute for Mathematical Sciences.
