Math and Computer Science

Students & Faculty Research COVID-19 Using Mathematical Modeling

“Mathematical modeling can tell you a lot about what’s going on with the coronavirus,” said Dr. Patrick Nelson , chair of LTU’s Mathematics and Computer Science Department (MCS). “It’s really wonderful because it’s without bias.”

“Mathematics and statistics play an important role in understanding the key pandemic parameters, such as the transmission and recovery rates, and determining the primary routes of transmission,” writes Dr. Matthew Johnston in describing COVID-19 Modeling at LTU. Together with fellow LTU faculty member Dr. Bruce Pell , Johnston has been leading a variety of student-centered activities at Lawrence Tech on the effects and trajectory of the COVID-19 pandemic.

“One of the main reasons I came here was that LTU’s academics are top tier.”


During June and July 2021, Johnston and Pell ran the National Research Experience for Undergraduates Program (NREUP) funded by the Mathematical Association of America . The program engaged five black students in vital mathematical research with the goal of creating an enduring environment of opportunity and inclusion for the black community in the Metro Detroit region. The program’s goal was to develop and analyze dynamical systems models of disease spread, primarily the spread of COVID-19, with a focus on its impact on the local black community. In Metro Detroit, and more broadly in the state of Michigan, the disease has taken a disproportionate toll on blacks than it has on whites--more than twice as high.


NREUP participants with their professors. From l to r: Antwan Green, Dr. Bruce Pell, Jalen Jackson, Steven Harris II, Noah Stamboulieh, Temidayo Ogunmodede, and Dr. Matthew Johnston

Steven Harris, a biomedical engineering student who expects to graduate in May 2022, was part of the seven-week program. Students were allowed to choose a topic related to COVID-19 on which to do their research. Harris is a residence assistant in Donley Hall. He built susceptible infected recovery models using LTU as his test population. He gathered data on quarantine capacity and mitigation rates. Harris predicted when schools would go over their limit for the number of students that could be quarantined in place and what it would take to slow the transmission from student to student, including athletes. He said, “Especially living during the first wave of COVID, it was great to have solid evidence of what could be possible to stay safe while on campus.”


Special lecture by Matthew Johnston on Disease Spread Modeling given to a Calculus class. 

Motivated by the work of one of the students from NREUP, MCS will continue its important research on the effects of COVID-19, this time assessing the impact of attending centers of religious worship on vaccine uptake. “Working with this student, the project will focus on incorporating heterogeneous populations or sub-populations in the dynamical models and what that tells us about the spread of COVID-19 throughout different parts of the United States,” said Pell. “One example of a sub-population is those attending/traveling to religious centers of worship.”   

In addition to the summer program, Johnston and Pell served as co-instructors for a course in mathematical epidemiology in spring 2021, where students learned about mathematical techniques used to understand, predict, and control the spread of infectious diseases, building and analyzing various mathematical models and using dynamical systems approaches. They also co-organized a seminar series starting in fall 2020 for LTU students and the broader community on quantitative aspects of COVID-19. The series featured public health experts and researchers from institutions such as Michigan State University, Georgia State University, and the Los Alamos National Laboratory as speakers.

“Mathematics and statistics play an important role in understanding the key pandemic parameters, such as the primary routes of transmission.”


“We can use math to tell the story [of COVID-19],” said Pell. “Everybody’s confused. Math can tell us where the virus is going, how it’s going, and what we can do about it. The general public doesn’t read the professional journals and can become easily confused and influenced by biased reporting in mass media. Here, we’re trying to demonstrate that, through mathematical analysis, we can have a positive impact on the disease’s trajectory.”

Students are at the forefront of the COVID-19 research happening at LTU. Parents can be proud that their students are conducting such important work, which will have practical application in their future careers.

Looking to the future, Pell continued, “The world is going to need a new type of college graduate; one that understands how mathematics can be used in other fields such as biology and epidemiology. At LTU, students are being prepared to be leaders in these important multidisciplinary fields.”

Andrea Houck, a senior with dual physics and math majors, can’t say enough good things about her LTU experience and her professors. “I’ve been really excited to discover that I really love math. I knew I wanted physics but when I transferred to LTU and Dr. Yelena Vaynberg introduced me to calculus and the math club , I was hooked.

“I’ve been involved in a lot of different research projects. That’s helped me develop the skills I’ll need in the future. I had the opportunity to learn skills in MATLAB , computer software useful for data analysis. I want to go on for a master’s in medical physics.”

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Andrea Houck

As part of a Student Research Award with Johnston and Pell in summer 2020, Houck examined “mask efficiencies in halting the spread of COVID.” She said of her results, “I found that the more efficient the mask and the more people who wear masks, the disease is reduced. Less people get sick and it takes a longer time to spread through the population.”

The summer award was made possible by LTU’s course-based research experience, or CRE , grant funded by the Howard Hughes Medical Institute . CRE is incorporated into STEM studies throughout LTU. Integrating research in undergraduate courses in different disciplines has led to several peer-reviewed articles in high-impact journals with LTU students as co-authors.

The mathematics department faculty and students continue to have a keen interest in the trajectory and path of COVID-19 and its variants and how to stem their tide. They plan to assess an ensemble modeling approach to the spread of infectious disease, vaccination strategies, and social feedback: we're putting together a grant proposal for assessing different types of disease forecasting models and the methods used to calibrate them to the data. This is something that, if funded, students can easily work on with a low barrier to entry.


Macomb County Covid-19 model prediction produced by Matthew Johnston.

They also plan to assess the social response to vaccination and its impact using mathematical modeling.

Harris, a future physician assistant, said, “I’ve already participated in four research projects at LTU. One of the main reasons I came here was that LTU’s academics are top tier. Johnston and Pell make learning fun and engaging; they’re invested in our projects and in making something that’s actually useful.”

Blue Devils basketball player and biomedical engineering major Aleksandar Ivanovic agrees that his LTU experience is preparing him for his future. His math and science courses, his applied research, and the understanding he’s experienced from his professors are feeding his vision as a biomedical engineer. “I just hope to use what I’ve learned to help people, and potentially save lives.”

by Renée Ahee

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