Many U.S. universities are embracing the hybrid teaching modality thanks to the start of the COVID19 vaccinations and availability of online teaching tools. This work presents a continuation of our previous research, in which we analyzed and developed a methodology to inhibit COVID-19 spread on a university campus. We simulate the virus spread on campus, comparing and models, and examine how diferent course policies can afect the number of infected students. We demonstrate that we can achieve a safer environment on campus by moving a certain number of courses with the highest centrality values. Additionally, we analyze how the student flow rate can help reduce the 0 value representing the metric of how many other people an infected individual could infect. This work also presents the simulation analysis of the opened public places on campus and the application of the sensitivity analysis to develop the most eficient approach determining the exact courses that need to be moved online. We conclude with the recommendations and analysis results.
and develop the procedures that help us make policies that provide a valuable input on which courses should be moved online, what to do with the public places like dining halls, and what the most important parameters are (through the sensitivity analysis in section 3) that afect the virus spread on campus.
We compared two diferent simulation methods and selected the model [
Our control group represents the number of students being infected, assuming that the semester
is fully online. The data we use come from the CDC [
The control group simulation results demonstrate that after 15 weeks in the fully online fall semester, the total number of infected students could be 374. In the following section, we are going to compare the control group’s results with the face-to-face semester under our proposed measures to move only certain courses online.
In this section, we simulate the virus spread in the pessimistic, normal, and optimistic scenarios (public places like the dining hall are assumed to be closed). To match our simulation as close as possible with the complexities of the real situation on campus, we focus on the pessimistic configuration as it describes the worst-case scenario. The following diagrams are built based on the pessimistic scenario with the initial 0 set to 3.2. The results of the normal and optimistic scenarios are also shown in table 1.
We performed several simulation experiments and would like to share the results under 3 diferent policies presented in figures 3, 4, and 5.
1. Policy #1: none of the courses are moved online and all students meet face-to-face. 2. Policy #2: five courses with the highest centrality are moved online.
3. Policy #3: ten courses with the highest centrality are moved online.
It can be seen that even under the most pessimistic circumstances, the number of infected people can be reduced by moving five courses with the highest sensitivity online compared with the control group. After moving 10 high sensitivity courses online, the number of infected students decreased by 15.5%, from 374 to 316.
Figure 1 demonstrates the diferent outcomes of moving a certain number of courses online in a pessimistic scenario relative to the control group (fully online semester).
We also simulated a special situation by closing certain classrooms every day with the highest student flow rate (figure 6). The expected 0 value decreased by 38.63%, from 3.2 (default) to 1.96, and the total number of infected students reduced to 115. We propose to move such classes to other available classrooms, resulting in the lowest infection rate with the number of infected students to be in the range from 115 to 374, depending on how many of those classes can be relocated.
One of the issues that are not addressed in the social network graph is the issue of students’ dining options. Considering that there are only a few places at Arcadia that could provide food for students, their closure could become an inconvenience for everyone. However, opening those buildings may bring students together again and speed up the spread of the virus, which does not conform to the notion of reducing the number of face-to-face courses to protect the health of students. Consequently, we also simulated the spread of the virus in the school if we did not close public places like the dining hall (assuming all possible students have lunch). For example, we studied each student’s schedule to determine if they could have lunch in the canteen at noon (there are around 650 such students), and then we added it as a “lunch course” in the social network to simulate the place where students may eat together. The expected value of 0 increased by 2,769% (from 3.2 (default) to 88.63), meaning that almost all the students would be infected. Figure 7 presents the simulation of opening dinning halls without moving any courses online.
To solve the dining problem, meals can be delivered to each student’s room or takeout meals without contact could be arranged. Also, while processing the data, we were able to determine the number of students that would possibly dine on campus at a given time because, for instance, they had a break between the morning and afternoon classes. Based on this information, Arcadia could estimate the outdoor seating needs at a given time and provide a suficient number of tables and chairs on campus, taking into consideration that not all students dine in public places on campus.
Additionally, other public places like gyms can set up isolation zones for each part of the equipment and limit the number of people using the gym at a time.
The purpose of this project is to reduce the number of infected students in a face-to-face semester as much as possible and make sure that the risk of being infected on campus is lower than the one in the local region, making it a safer educational environment. At the same time, we hope to change the curriculum (shift a certain number of courses online) as little as possible. Therefore, we focus on developing the most eficient approach to determine the courses that need to be moved online. To better understand our results from section 2, we performed a sensitivity analysis to determine the changes and correlations in our model depending on the input variables simulating the virus transmission. 3.1. Sensitivity results for parameters in 0 simulation We compared the efects of each parameter on the results with parameter changes of -30%, -10%, 10%, and 30%, and presented them on figure 8, in which: • is the speed rate at which students change from being “susceptible” to being “infectious” (i.e., the infection rate). Its value can be roughly calculated by the product of 0 and the recovery rate. • is the speed rate at which students change from being “exposed” to being “infectious” (i.e., the incubation rate). Its function is defined as 1/ . • is the speed rate at which students change from being “infectious” to being “recovered” (i.e., the recovery rate). Its function is defined as 1/ .
The parameter can be simply understood as the number of days that a student can continuously infect others before being tested (and later quarantined) or beginning to show symptoms. Therefore, it is particularly important to detect asymptomatic or latent patients as early as possible, directly reducing the average number of infections per patient. Therefore, it is necessary for the schools to conduct regular tests when possible. With enough testing equipment, smaller campuses like Arcadia could eficiently conduct virus tests, reflecting an advantage of school opening because students can be constantly organized and tested. Regular testing is comparatively more dificult to implement in the wider community, often leading to family and community clustering infections.
Based on the simulation results, sensitivity analysis, and rectified centrality formula, we can
answer the following questions that we defined in the previous work [
Question #1: “would schools be able to stay open during COVID-19 by moving high sensitivity classes and students online?” The simulation results demonstrate that it is possible, as long as the school follows the policies we proposed and all assumptions we made are true. Even under a pessimistic 0 set to 3.2, the number of infected students at Arcadia could be 316 after moving 10 classes with the highest centrality online, which is still lower than 374 (the predicted value of infected students made if the semester is fully online). But this result is based on the assumption that students would follow safety practices, reduce other forms of contact as much as possible in addition to basic academic activities, and all students, faculty, and staf could be tested before returning to and while being on campus. We found that even if all students take classes online, they will still be exposed to an environment where 0 equals 3 and 374 students could get infected at the end of the semester. Therefore, returning to school based on the proposed policies can achieve a lower infection rate and provide better protection to students compared with the fully online semester. However, it should be noted that the school’s dining places and gyms should be closed, otherwise almost all students would be infected.
Question #2: “How many students would be infected compared to the model without converting classes to an online format?” If we do not convert any courses to the online format, the number of infected students in the optimistic scenario would be 120, in the normal scenario it would be 217, and in the worst-case pessimistic scenario it would be 456.
Some of the notable characteristics of the data that we worked with are presented below.
• The average and maximum numbers of students that one student may be exposed to
while taking classes on campus throughout a week are: = 175; = 66.
• Courses with the respective values of diferent degrees of centrality were shown in a
table in [
• There are a total of 61,186 pairs of students who are directly connected.
Our final recommendations based on the simulation results and analysis are presented below.
• It is possible to reduce the 0 value by moving high sensitivity courses online.
• The dining places should be closed. We proposed alternative options in section 2.4.
• Temperature-measuring devices [
We would like to thank the Computer Science and Math Department, Arcadia University, for providing support and help during this research.