key: cord-0820333-a72ok3yv authors: Hartvigsen, G. title: Network assessment and modeling the management of an epidemic on a college campus with testing, contact tracing, and masking date: 2021-04-09 journal: nan DOI: 10.1101/2021.04.06.21255015 sha: b414f40d9033d5febcf3b2e34db84dbbfbd56742 doc_id: 820333 cord_uid: a72ok3yv There remains a great challenge to minimize the spread of epidemics. This may be particularly true on densely populated, residential college campuses. To construct class and residential networks I used data from a four-year, residential liberal arts college with 5539 students. Equal-sized random networks also were created for each day. Different levels of compliance with mask use (none to 100%), mask efficacy (50% to 100%), and testing frequency (daily, or every 2, 3, 7, 14, 28, or 105 days) were assessed. Tests were assumed to be only 90% accurate and positive results were used to isolate individuals. I also tested the effectiveness of contact tracing and subsequent quarantining of neighbors of infectious individuals. I used class enrollment and residence data from a college with 5539 students to analyze network structure and test the epidemic potential of the infectious disease agent SARS-CoV-2. Average path lengths were longer in the college networks compared to random networks. Students in larger majors generally had shorter average path lengths. Average transitivity (clustering) was lower on days when students most frequently were in class (MWF). Degree distributions were generally large and right skewed, ranging from 0 to 719. Simulations began by inoculating twenty students (10 exposed and 10 infectious) with SARS-CoV-2 on the first day of the fall semester and ended once the disease was cleared. Transmission probability was calculated based on an R0 = 2:4. Without interventions epidemics resulted in most students becoming infected and lasted into the second semester. On average students in the college networks experienced fewer infections, shorter duration, and lower epidemic peaks that occurred compared to dynamics on equal-sized random networks. The most important factors in reducing case numbers were the proportion masking and the frequency of testing, followed by contact tracing and mask efficacy. The paper discusses further high-order interactions and other implications of non-pharmaceutical interventions for disease transmission on a residential college campus. There remains a great deal of interest in understanding and predicting the dynamics of 2 the spread of the SARS-CoV-2 virus and similar infectious agents through populations. 3 Analytical models are useful for estimating spread rates and extent of epidemics but 4 lack the realistic structure of how people actually encounter each other. Network-based 5 models, on the other hand, allow for discrete modeling of epidemics through more 6 realistically-structured populations [1] [2] [3] . These models, however, usually rely on 7 generalizations about the structure of networks, such as being based on a famous 8 network (e.g., [4] ). The current work attempts to overcome this by using actual 9 enrollment data for a medium-sized residential, liberal arts college. 10 A variety of models have been used to investigate potential spread and containment 11 using different non-pharmaceutical interventions [5] . The results suggest that 12 government-mandated lock downs, for instance, are essential to work toward reducing 13 COVID-19's spread (achieving an R 0 < 1.0). However, the latter has been criticized for 14 not incorporating the benefits from practices such as contact tracing [6, 7] . 15 There are many studies that have demonstrated the effectiveness of different 16 non-pharmaceutical interventions for the containment of SARS-CoV-2 among people. 17 Masks, for instance greatly reduce the emissions of aerosolized droplets that are the 18 leading cause of transmission [8, 9] . Additionally, testing and subsequent quarantining 19 has been shown to be effective in reducing transmission rates [10, 11] and are having 20 effects on other directly transmitted diseases [12] . In this paper I explore the interactive 21 effects of COVID-19 testing, isolation, quarantining, and different proportions of people 22 using masks that differ in efficacy within a real college network. The model relies on 23 actual enrollment data in classes from a college with more than 5500 students. 24 Much remains unknown about the effectiveness of these interventions, such as 25 masking [13] . In particular, there are differences between different types of masks, 26 ranging from the common bandanna (neck gator) to N95 respirators [9, 14] . Because of 27 this it is important to examine how masks with different efficacies might influence the 28 spread of COVID-19 through a population. In addition, there are differences in the 29 extent to which people use masks and wear them appropriately. In one study 86.1% of 30 adults ranging in age from 18-29 chose to wear masks [15] . Despite this encouraging use 31 of non-pharmaceutical interventions the pandemic has not been contained. 32 The US Centers for Disease Control and Prevention (CDC) has provided guidelines 33 for institutions of higher education for safe operations [16] . Included in these 100% effective and used by everyone). It is the hope of this work that we can better understand and predict the dynamics of 40 infectious diseases and the effect on control measures in residential college communities. 41 Anonymized data for a two-semester academic year (2019-2020) were acquired that 43 included class enrollments and local addresses for 5539 students [17] . Networks were 44 constructed for each day of the week for each semester. Class sizes ranged from 1 to 351 45 students. Weekend networks contain only housing data. Daily networks ranged from 46 3108 to 4919 students that were connected with between 109,000 to 305,000 edges, 47 connecting students who were either enrolled in the same class or lived at the same 48 address. Multiple edges were permitted. No faculty or instructors were included in the 49 networks. In addition, equal-sized random networks were created for each day. I calculated degree distributions, average path lengths, and average clustering 51 coefficients (transitivity) for the college and random networks for each day of the week 52 for both fall and spring semesters. An SEIRIQ network model (states include susceptible, exposed, infectious, recovered, 54 isolated, and quarantined) was developed to simulate the spread of the SARS-CoV-2 55 virus through a population of undergraduate students (Fig 1) . The network changed for 56 each day of the week as students attended their various classes. On weekends students 57 were assumed to only come into contact with their house mates. Fall and spring 58 semesters were assumed to continue without interruption. At the beginning of the fall 59 semester 20 students were assumed to begin classes infected with the virus (ten 60 categorized as exposed and ten infectious). Students remained in the non-infectious 61 exposed class for two days. After a 10 day infectious period ended individuals would 62 enter a recovered state and could not be reinfected. The basic reproductive number (R 0 ) 63 was set at 2.4 [18] which follows an earlier report which suggested the same rate [5] . These and additional parameters for the model are provided in Table 1 . Simulations 65 ended when the disease was cleared or there were no remaining susceptible neighbors of 66 infectious individuals. The model assumes no individuals are able to become reinfected 67 which has been found to be relatively rare [19] . Model, statistics, and network 68 construction and analysis were completed using R [20] and the igraph package [21] . Simulations were run to compare spread under unmitigated conditions between the 70 student and random networks (no masking or testing). Individuals were initially 71 susceptible with 10 individuals randomly inoculated as exposed with an additional 10 72 individuals inoculated as infectious. Exposed individuals became infectious after two 73 days and remained infectious for 10 days (see Table 1 ). testing (see Table 1 ). Students were not tested if they were currently awaiting test 80 results or in either isolation, quarantine, or recovered. Test results were evaluated one 81 day after testing with a 90% positive accuracy rate (false positives were not considered). 82 If testing was being used then students that were infectious at the time of the test were 83 isolated for two weeks. If contact tracing occurred then all susceptible neighbors were 84 quarantined for two weeks. The model treats quarantine as complete with no contacts 85 allowed. Students that were in the exposed state when tested then their test result was 86 treated as a negative and were returned to the network and allowed to move to the 87 infectious state. After 10 days in the infectious state students were moved into a 88 recovered class and could neither receive nor share the virus with neighbors. The transmission probability (T d,s ) was calculated for each day of the week (d) for 90 each semester (s). This probability was used to determine the likelihood that an 91 infectious individual would pass the virus to a susceptible neighbor on a given day. T d,s 92 was determined using the following relationship: where K d,s is the median degree of the network on day d of each semester (s) [4] . I begin with a comparison evaluating the structural differences between the college and 103 random networks. This includes the degree distributions and clustering coefficients as 104 well as the average path lengths for all students and grouped by majors. These metrics 105 play important roles for the overall dynamics of disease transmission. This is followed by 106 a discussion of the results from simulating disease transmission through these networks. 107 The college network structure 108 The college networks include course enrollments for Monday -Friday plus the housing 109 data for all days of the week over both fall 2019 and spring 2020 semesters. Students 110 were assumed to interact only with their housemates on weekends. These networks, 111 were strikingly different from the random networks for each day of the week and 112 between semesters (see Fig 2) . These structural differences led to significant differences 113 in the dynamics of disease spread between the college and random networks (discussed 114 below). The housing network includes 89% of students (e.g., students not reporting 115 off-campus residences). A majority of students can be seen living in pairs (dyads in Fig 116 2 ). Undoubtedly, weekend and evening gatherings could contributed substantially to 117 epidemic spread. College Network Random Network The number of connections (degree) for individuals in the college networks ranged from 120 0 to 719 and varied from day to day and were right skewed (Fig 3) , with most 121 individuals having a total degree less than 100 each day. A small number of students 122 had a zero degree on a day in which they had no classes and happened to not have their 123 housing location reported. On the weekend ("SS" in Fig 3) we can see that a few The average path length (APL) is a metric that summarizes the average number of 128 steps from each student to all other students through both the enrollment and housing 129 networks. APL varied by day of week (Fig 4) . Most notably, students are very highly 130 connected with fewer than three steps separating students, on average. Some differences 131 are apparent between semesters, particularly between MWF and TR classes. Average 132 path lengths are longer in the college network compared to the random network due to 133 clustering that takes place within majors. Additionally, we can see that students in 134 different majors had variable average path lengths with no clear pattern related to size 135 of major ( Fig 5) . (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. random networks (Fig 7) . The dynamics exhibited periodicity on a weekly schedule due 152 to restricted spread on weekends when individuals in the model mix only with those with 153 which they reside. As a result, relatively few individuals become exposed over weekends. (Table 2) . Additionally, all higher-order 159 interactions were statistically significant (not shown in Table 2 ). I found that testing, 160 and subsequent isolation and quarantining of contacts, significantly reduced the total 161 number of infections, accounting for a combined 27% of the overall variance. The effect 162 is quite large for even small levels of testing and subsequent isolation of individuals who 163 test positive, followed by quarantining of neighbors. I found a significant reduction in 164 the numbers of individual infected with as little as 0.5% of the population tested daily 165 (students testing once per month, Fig 8) . In the absence of interventions (testing and masking) disease prevalence reached its 167 highest levels seen in all simulations. Overall, the college, with its higher APLs and 168 clustering coefficients, exhibited fewer infections than seen in the random networks 169 (Table 3) . Additionally, the epidemics on the college networks reached their peaks and 170 ended later than those on random networks and resulting in fewer infected individuals. 171 An additional challenge for college health providers is the result that the epidemic peak 172 on this campus occurred after just one month and involved over 25% of the student 173 April 6, 2021 7/16 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 9, 2021. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. . Results here concur (Fig 8) although, numerically, fewer individuals 178 were infected by testing daily. There was no significant difference between the number 179 April 6, 2021 9/16 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. However, from an implementation standpoint I found that the number of tests needing 181 to be administered in the college network population was highest when tests were 182 administered every other day (Fig 9) . This is due to the high reproductive rate of 183 SARS-CoV-2 (R 0 = 2.4) that allow the virus to spread more than when testing 184 occurred daily. The fewest tests were required when testing was conducted daily and 185 when done just once per student per semester, although the latter was the least effective 186 method for controlling COVID-19 (Fig 8) . Table 3 . Comparison of unmitigated spread on the college vs random networks. The four main response variables are presented as means (± 95% CI). No masking or testing was done. All eight samples were normally distributed. All responses were significantly different between the college and random networks using a t-test (df = 18). Note that the outbreaks were completed after approximately one semester (105 days) and infected an average of 63% and 76% of the college and random network individuals, respectively. These simulations include only tests with contact tracing and no masking using the college networks. The average number of tests per person was greatest when individuals were tested every other day. This was far greater than when individuals were tested daily because individuals that tested positive were isolated, not tested during this period and most effectively curtailed the outbreak. Error bars are ± 95% confidence intervals. Samples sharing letters are not statistically different. An additional 19% is explained by the interactive effects of the number of people 188 tested and the proportion of individuals that mask, regardless of the efficacy of masks, 189 which ranged from 50% to 100% effective. The effects of masking Masking significantly reduced the number of infected individuals in these populations. 192 Importantly, I found a significant interaction between the proportion of people masking 193 and the efficacy of the masks (Fig 10, Table 2 ). As can be seen in this figure, changing 194 from no masking to even using masks that are 50% effective at blocking the 195 transmission greatly reduced the number of infections. April 6, 2021 11/16 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 9, 2021. The number of individuals that became infected under different levels of masking and mask efficacy for both the college and random networks. This three-way interaction was statistically significant (F = 74.14; df = 12, 5760; p < 0.001) along with the two-way interactions within network types. Without masking more students contracted the disease on the random networks but masking proved less effective, comparatively, on the college network due to the high clustering of students. Error bars are ± 95% confidence intervals. Which students contract COVID- 19? 197 Unfortunately, essentially all the students are vulnerable and likely to contract When a disease, such as COVID-19, enters a college population there exists a variety 218 of challenges to minimizing its spread. In this work I investigated the effects of various 219 methods to minimize disease spread. The findings suggest that the risk of disease 220 spread is reduced significantly by the actual structure of students who are non-randomly 221 enrolled in classes, mainly with members of the same majors. This appears to be largely 222 there was clearly an increased risk of students contracting a disease like COVID-19 from 228 larger classes. Admittedly, entering into a non-voluntary 14-day quarantine period is disruptive to 230 everyone, particularly college students. In this model, too, students were completely 231 compliant during the quarantine period. When implementing frequent testing of 232 students in the model many students ended up in quarantine. This greatly disrupts 233 learning environments. There is evidence that shorter quarantine periods may be 234 effective [27] . Additionally, this model assumes a relatively rapid turn around on testing 235 results (1 day). Interestingly, testing students every day resulted in very low numbers of 236 tests administered because infectious individuals were rapidly identified and isolated, All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 9, 2021. the use of even low efficacy masks the epidemic can be well contained. The current work does not model the effects of social distancing as an effective 248 non-pharmaceutical intervention. Clearly, the level of concern by students can vary 249 greatly and this was accounted for through the testing of mask efficacy (from 50 -100% 250 effectiveness). This model calculates a transmission probability for all students each day. 251 With this approach it is assumed that students all share the same likelihood of either 252 infecting others or being infected by others. It would be interesting to know how 253 important these assumptions are in affecting the outcomes reported here. Students on a college campus generally reside in very well connected networks by 256 attending classes and living in residence halls. With a high reproductive rate for a 257 directly transmitted disease agent, such as SARS-CoV-2 students attending a residential 258 college are at a high risk of spreading and contracting such a disease. I found that the 259 actual structure of the college network itself was sufficient to reduce the spread of the 260 disease agent. This was due to students in majors taking classes together, leading to 261 increased average path lengths and higher clustering coefficients compared to 262 randomized networks. Additionally, wearing masks and utilizing frequent testing and 263 contact tracing that leads to isolation and quarantine can greatly reduce spread in such 264 a community. Even the use of poorly functioning masks alone greatly reduced 265 transmission. Finally, I found that class sizes greater than 40 students resulted in high 266 proportions of those students contracting the disease. Therefore, working to manage the 267 Collective dynamics of "small-world" networks Emergence of scaling in random networks Dynamical patterns of epidemic outbreaks in complex heterogeneous networks Network structure, and vaccination strategy and effort interact to affect the dynamics of influenza epidemics Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand, Imperial College COVID-19 Response Team Conact tracing and disease control Impact of non-pharmaceutical interventions County-Level COVID-19 Incidence in Counties With and Without a Mask Mandate -Kansas Efficacy of face masks, neck gaiters and face shields for reducing the expulsion of simulated cough-generated aerosols Modelling the impact of testing, contact tracing and household quarantine on second waves of COVID-19 Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe The impact of COVID-19 nonpharmaceutical interventions on the future dynamics of endemic infections What the data say about wearing face masks Visualizing the effectiveness of face masks in obstructing respiratory jets Scientific Brief: Community Use of Cloth Masks to Control the Spread of SARS-CoV-2 Centers for Disease Control and Prevention. Considerations for Institutions of Higher Education Special thanks to Dr. Julie Rao, Director, Office of Institutional Research Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2. Emerging Infectious Diseases COVID reinfections are unusual -but could still help the virus to spread R: A language and environment for statistical computing. R Foundation for Statistical Computing The igraph software package for complex network research Temporal dynamics in viral shedding and transmissibility of COVID-19 Assessment of SARS-CoV-2 Screening Strategies to Permit the Safe Reopening of College Campuses in the United States An investigation of transmission control measures during the first 50 days of the COVID-19 epidemic in China Optimal COVID-19 quarantine and testing strategies size of classes would likely reduce the incidence of transmissible diseases on college 268 campuses.