Students create COVID-19 math model


Photo credit/ Jeremy Stanton

Ellen Frantz, News Editor

Two students, along with Professor of Mathematics Dr. Craig Johnson, have built a model to track the spread of the coronavirus throughout Northeastern Pennsylvania.

Senior math majors Jack DeGroot and Heather Kwolek have been tracking COVID-19 since the end of June by using calculus to create a Susceptible, Infectious and Recovered (SIR) model. Through this model, they found the rate of change from someone susceptible to the virus who then becomes infected and recovers.

“We tried to simulate Marywood’s population, and we had to assume our initial infectant,” said Kwolek. “We would assume what the CDC says was the average amount of people infected and that’s how we were able to graph and see how many people would be infected over a time period of 60 days, two months and such.”

Their model is made up of four graphs representing the measures in a SIR model. Within these four graphs were 1,000 people they used to represent any random group of 1,000 people on Marywood’s campus. Each graph had a different number of people who came to campus infected and had different infection rates.

Many other schools have been using this SIR model to track the spread of COVID-19, such as Princeton, Harvard and even the University of Geneva in Switzerland.

“The SIR [model] has been expanded upon in a lot more complicated ways,” said Johnson. “But what I wanted to do was introduce these two students, who are excellent math majors, to a current application of their differential equations course.”

As for the model’s predictions, Kwolek said Marywood’s current number of positive COVID cases is a lot fewer than the model predicted, but the University of Scranton’s numbers are following the model more closely since it predicted there would be 50 positive cases after 10 days.

“‘What we saw was concerning,” said Kwolek. “We thought by September 15 that we would probably have to shut down campus again from looking at the University of Scranton; however, [their campus shutting down] doesn’t seem like an unreasonable guess.”

The graph determined that more cases would occur when more students come to campus already having the disease, something that DeGroot said he believes could have easily been prevented.

“In the one model, we have 20 people coming to Marywood and Northeastern PA with COVID already and in another model we have 50 people coming, which causes a very steep line of infections,” said DeGroot.

A main takeaway from the project, according to DeGroot, is that testing students before they were allowed to return to campus would not only help decrease the number of students who were coming to school sick, but would also decrease the rate at which the virus spreads.

According to DeGroot, the rate of the contagiousness of COVID-19 is 1.1. Anything over 1.0 means a pandemic will occur. So, if 20 people came to campus with the disease, 100 people could get sick within 45 days.

The students plan to continue their work on the model and want to add the real number of positive cases at Marywood. They also want to see the effect social distancing and masking has on the number of positive cases now that there are COVID-positive students actually at the school.

They especially want to work with the number of people whose tests came back positive but who were not showing symptoms, or those who are sick but never got tested.

“Without constant testing, we can’t really determine how many people out of the infected and recovered would be showing symptoms,” said Kwolek.

Dr. Johnson said they’ll never know how accurate their model is due to the lack of testing.

“You have to be doing random testing to get valid information about how many people truly are positive,” says Dr. Johnson. “You can’t just be testing people who are showing symptoms since so many people are asymptomatic. That is not going to give you true results.”

The model shows the number of cases over 50 days, so the model can be updated every 50 days to reflect what is happening at that time.

Dr. Johnson said he has shared the model with both Marywood President Sr. Mary Persico, IHM, Ed.D. and other faculty members. The model helped put into perspective how hard Marywood needed to work to keep their students safe.

“She showed them to the doctor she was consulting with and they said [the graphs] were spot on,” said Dr. Johnson. “They were absolutely the right model to be using.”

Persico is very grateful for Dr. Johnson and the students for working on and sharing their model with her.

“We have to understand how this spreads and that’s really going to help us understand what we have to do not to have it spread to each other.” said Persico of the model. “The more people can know what [the] research is showing, the better off we’ll be.”

Persico said the model helped show Marywood administrators how serious this virus was to the local community and informed them on how quick it spreads, which led to the installation of UV air filters in all of the lighting fixtures around campus.

“We didn’t take any of this lightly,” said Persico. “We knew we had to come back to campus but the research told us that we can’t allow students to bunch up so we decided to bring them back only one-third of the time so in that sense we did look at his research.”

In the end, the students researched other schools who made COVID-19 models to see if they could impact policy change in both their school and their state.

“We wanted to try to prove to Sister Mary that this model is legitimate and that other universities are using this exact same model to cancel their school and go all online,” said DeGroot.

DeGroot said it is too early to tell how accurate their model is to the Marywood community and its number of COVID cases, but said he believes the number of cases within the next few weeks will really show how close their predictions are.

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