Evaluation of infection risk for SARS-CoV-2 transmission on university campuses

Figures & data

Table 1. Descriptions of the confined spaces.

Scenario	Dormitory	Classroom	Gym	Library	Dining hall
Floor area (m^2)	20	80	8000	300	1050
Height (m)	3	3.7	19.5	16	4.8
Volume (m^3)	60	296	156000	4800	5040
Ventilation rate (ACH)	0.5 (NV)	6.08 (MV)	4.5 (MV)	2 (MV)	3 (MV)
Number of infectors	1

Table 2. Detailed information of the exposure scenarios.

Scenarios	Dormitory	Classroom	Gym	Library	Dining hall
Exposed subject	Sleep or talking	Study or talking	Playing basketball	Study or whisper	Eating
Pulmonary ventilation rate (m^3/h) $(p)$	0.49	1.38	3.3	0.49	1.38
Total susceptible population $(N)$	4	61	3511	600	200
Total exposure time $(t)$	8 h	1.5 h	2 h	4 h	0.5 h

Table 3. The quanta values of common airborne pathogen.

Airborne pathogen	Scenario	Quanta value (quanta/h)	Data resource
Influenza	School, train	LN (66.91,1.53)	(Liao, Chang, and Liang 2005)
		3.5	(Gao et al. 2012)
	Aircraft	15 ∼ 128	(Rudnick and Milton 2003)
		28	(Gao, Li, and Leung 2009)
		LN (68.67,1.52)	(Liao, Chen, and Chang 2008)
	Hospital	515	(To and Chao 2010)
	Gym	76.18	(Andrade et al. 2018)
	All	100	(Azimi and Stephens 2013)
Rhinovirus	All	0.6 ∼ 7.8	(Rudnick and Milton 2003)
Tuberculosis	Office	12.7	(Nardell et al. 1991)
		13	(Basu and Galvani 2008)
		250	(Catanzaro 1982)
	Prison	1	(Johnstone-Robertson et al. 2011)
		1.25	(Urrego et al. 2015)
		10	(Mushayabasa 2013)
		12.7	(Hella et al. 2017)
	Community	1	(Wood et al. 2010)
	Gym	12.7	(Andrade et al. 2018)
	Hospital	1	(Noakes and Sleigh 2009)
		1.3	(Saab 1997)
		8.2	(Escombe et al. 2007)
	Market	1.25	(Hella et al. 2017)
	Café, care facilities	17.58	(Furuya, Nagamine, and Watanabe 2009; Furuya 2013)
	Cell block	30	(Cooper-Arnold et al. 1999)
	All	1.25 ∼ 60	(Beggs et al. 2003)
SARS	Hospital	LN (28.94, 2.66)	(Liao, Chen, and Chang 2008)
H1N1	Aircraft	50 ∼ 128	(Wagner, Coburn, and Blower 2009)
	Car	67	(Knibbs, Morawska, and Bell 2012)
Small pox	School	2	(Gao, Wei, Lei, et al. 2016)
Measles	School	8	(Riley, Murphy, and Riley 1978)
		93	(Riley, Murphy, and Riley 1978)
	Aircraft	LN (106.75, 1.93)	(Liao, Chen, and Chang 2008)
chickenpox	Aircraft	LN (59.07,1.99)	(Liao, Chen, and Chang 2008)

Fig. 1. Viral load in different specimens.

Fig. 2. Viral load distribution: (a) Histogram and Fitting Curve; (b) Normal Q-Q Plot.

Fig. 3. Droplet concentrations fitting curve.

Fig. 4. Natural logarithm of the quanta generation rate under exposure scenarios.

Fig. 5. The variations of $\mathit{c}(\mathit{t})$ and $\mathit{R}:$ (a) Dormitory; (b) Classroom; (c) Gym; (d) Library; (e) Dining hall.

Fig. 6. Estimated ${\mathit{R}}_0$ with exposure time for the exposure scenarios.

Fig. 7. The variations of estimated infection risk with ventilation rate: (a) Dormitory; (b) Classroom.

Fig. 8. ${\mathit{R}}_0$ with the different susceptible number and stay time.

Table 4. Parameters of the control measures used in the infection risk model.

Parameters	Value	Symbol/Unit	Data resource
Surgical mask	N (45, 3.1)	${\eta }_s\mathrm{ }(\mathrm{\%})$	(Gammaitoni and Nucci 1997)
Dental mask	61	${\eta }_s\mathrm{ }(\mathrm{\%})$	(Weber et al. 1993)
Homemade mask	70	${\eta }_s\mathrm{ }(\mathrm{\%})$	(Davies et al. 2013)
N95 mask	99	${\eta }_s\mathrm{ }(\mathrm{\%})$	(Lee, Grinshpun, and Reponen 2008)
UVGI	N (12.0, 1.3)	${h_u\mathrm{ }(h}^{-1})$	(Xu et al. 2005)
HEPA filtration	12	$h_r\mathrm{ }(h^{-1})$	(CDC 2003; Liao, Lin, and Cheng 2013)

Fig. 9. The variations of estimated $\mathit{R}$ and ${\mathit{R}}_0$ under combined engineering measures: (a) Dormitory;(b) Classroom; (c) Gym; (d) Library; (e) Dining hall.

Fig. 10. The variations of estimated $\mathit{R}$ and ${\mathit{R}}_0$ under some typical masks in the classroom.

Fig. 11. Comparison of quanta generation rate in different scenarios.

Liao, C.-M., C.-F. Chang, and H.-M. Liang. 2005. A probabilistic transmission dynamic model to assess indoor airborne infection risks. Risk Analysis: An Official Publication of the Society for Risk Analysis 25 (5):1097–107. doi:https://doi.org/10.1111/j.1539-6924.2005.00663.x

 PubMed Web of Science ®Google Scholar

Gao, X., Y. Li, P. Xu, and B. J. Cowling. 2012. Evaluation of intervention strategies in schools including ventilation for influenza transmission control. Building Simulation 5 (1):29–37. doi:https://doi.org/10.1007/s12273-011-0034-7

 Web of Science ®Google Scholar

Rudnick, S. N., and D. K. Milton. 2003. Risk of indoor airborne infection transmission estimated from carbon dioxide concentration. Indoor Air 13 (3):237–45. doi:https://doi.org/10.1034/j.1600-0668.2003.00189.x

 PubMed Web of Science ®Google Scholar

Gao, X., Y. Li, and G. M. Leung. 2009. Ventilation control of indoor transmission of airborne diseases in an urban community. Indoor and Built Environment 18 (3):205–18. doi:https://doi.org/10.1177/1420326X09104141

 Web of Science ®Google Scholar

Liao, C. M., S. C. Chen, and C. F. Chang. 2008. Modelling Respiratory Infection Control Measure Effects. Epidemiology and Infection 136 (3):299–308. doi:https://doi.org/10.1017/S0950268807008631

 PubMed Web of Science ®Google Scholar

To, G. N. S., and C. Y. H. Chao. 2010. Review and comparison between the Wells-Riley and dose-response approaches to risk assessment of infectious respiratory diseases. Indoor Air 20 (1):2–16. doi:https://doi.org/10.1111/j.1600-0668.2009.00621.x

 PubMed Web of Science ®Google Scholar

Andrade, A., F. Dominski, M. Pereira, C. Liz, and G. Buonanno. 2018. Infection risk in gyms during physical exercise. Environmental Science and Pollution Research International 25 (20):19675–86. doi:https://doi.org/10.1007/s11356-018-1822-8

 PubMed Web of Science ®Google Scholar

Azimi, P., and B. Stephens. 2013. HVAC filtration for controlling infectious airborne disease transmission in indoor environments: Predicting risk reductions and operational costs. Building and Environment 70:150–60. doi:https://doi.org/10.1016/j.buildenv.2013.08.025

 PubMed Web of Science ®Google Scholar

Nardell, E. A., J. Keegan, S. A. Cheney, and S. C. Etkind. 1991. Airborne infection. Theoretical limits of protection achievable by building ventilation. The American Review of Respiratory Disease 144 (2):302–6. doi:https://doi.org/10.1164/ajrccm/144.2.302

 PubMed Web of Science ®Google Scholar

Basu, S., and A. P. Galvani. 2008. The transmission and control of XDR TB in South Africa: An operations research and mathematical modelling approach. Epidemiology and Infection 136 (12):1585–98. doi:https://doi.org/10.1017/S0950268808000964

 PubMed Web of Science ®Google Scholar

Catanzaro, A. 1982. Nosocomial tuberculosis. The American Review of Respiratory Disease 125 (5):559–62. doi:https://doi.org/10.1164/arrd.1982.125.5.559

 PubMed Web of Science ®Google Scholar

Johnstone-Robertson, S., S. D. Lawn, A. Welte, L.-G. Bekker, and R. Wood. 2011. Tuberculosis in a South African prison-a transmission modelling analysis. South African Medical Journal 101 (11):809. doi:https://doi.org/10.7196/SAMJ.5043

 PubMed Web of Science ®Google Scholar

Urrego, J., A. I. Ko, A. da Silva Santos Carbone, D. S. G. Paião, R. V. E. Sgarbi, C. W. Yeckel, J. R. Andrews, and J. Croda. 2015. The impact of ventilation and early diagnosis on tuberculosis transmission in Brazilian prisons. The American Journal of Tropical Medicine and Hygiene 93 (4):739–46. doi:https://doi.org/10.4269/ajtmh.15-0166

 PubMed Web of Science ®Google Scholar

Mushayabasa, S. 2013. Application of Wells–Riley equations on a mathematical model for assessing the transmission of tuberculosis in prison settings. International Journal of Modeling, Simulation, and Scientific Computing 4 (3):1350010. doi:https://doi.org/10.1142/S1793962313500104

 Google Scholar

Hella, J., C. Morrow, F. Mhimbira, S. Ginsberg, N. Chitnis, S. Gagneux, B. Mutayoba, R. Wood, and L. Fenner. 2017. Tuberculosis transmission in public locations in Tanzania: A novel approach to studying airborne disease transmission. Journal of Infection 75 (3):191–7. doi:https://doi.org/10.1016/j.jinf.2017.06.009

 PubMed Web of Science ®Google Scholar

Wood, R., S. Johnstone-Robertson, P. Uys, J. Hargrove, K. Middelkoop, S. D. Lawn, and L.-G. Bekker. 2010. Tuberculosis transmission to young children in a South African community: Modeling household and community infection risks). Clinical Infectious Diseases 51 (4):401–8. doi:https://doi.org/10.1086/655129

 PubMed Web of Science ®Google Scholar

Noakes, C. J., and P. A. Sleigh. 2009. Mathematical models for assessing the role of airflow on the risk of airborne infection in hospital wards. Journal of the Royal Society, Interface 6 (Suppl. 6):S791–S800. doi:https://doi.org/10.1098/rsif.2009.0305.focus

 PubMed Web of Science ®Google Scholar

Saab, S. 1997. Infectiousness of air from a tuberculosis ward: Ultraviolet irradiation of infected air: Comparative infectiousness of different patients: Riley RL, Mills CC, O'Grady F, Sultan LU, Wittstadt F, Shivpuri DN. Am Rev Respir Dis 1962;85:511-25. American Journal of Infection Control 25 (1):65–6. doi:https://doi.org/10.1016/S0196-6553(97)90057-2

 Google Scholar

Escombe, A. R., C. C. Oeser, R. H. Gilman, M. Navincopa, E. Ticona, W. Pan, C. Martínez, J. Chacaltana, R. Rodríguez, D. A. J. Moore, et al. 2007. Natural ventilation for the prevention of airborne contagion. PLoS Medicine 4 (2):e68. doi:https://doi.org/10.1371/journal.pmed.0040068

 PubMed Web of Science ®Google Scholar

Furuya, H., M. Nagamine, and T. Watanabe. 2009. Use of a mathematical model to estimate tuberculosis transmission risk in an Internet café. Environmental Health and Preventive Medicine 14 (2):96–102. doi:https://doi.org/10.1007/s12199-008-0062-9

 PubMedGoogle Scholar

Furuya, H. 2013. Estimation of environmental control measures for tuberculosis transmission in care facilities for the elderly. The Tokai Journal of Experimental and Clinical Medicine 38 (4):135–41.

 PubMedGoogle Scholar

Cooper-Arnold, K., T. Morse, C. Pettigrew, M. Hodgson, R. Wallace, J. Clive, and J. Gasecki. 1999. Occupational tuberculosis among deputy sheriffs in Connecticut: A risk model of transmission. Applied Occupational and Environmental Hygiene 14 (11):768–76. doi:https://doi.org/10.1080/104732299302198

 PubMedGoogle Scholar

Beggs, C. B., C. J. Noakes, P. A. Sleigh, L. A. Fletcher, and K. Siddiqi. 2003. The transmission of tuberculosis in confined spaces: An analytical review of alternative epidemiological models. The International Journal of Tuberculosis and Lung Disease: The Official Journal of the International Union against Tuberculosis and Lung Disease 7 (11):1015–26.

 PubMed Web of Science ®Google Scholar

Wagner, B., B. Coburn, and S. Blower. 2009. Calculating the potential for within-flight transmission of influenza A (H1N1). BMC Medicine 7:81 doi:https://doi.org/10.1186/1741-7015-7-81

 PubMed Web of Science ®Google Scholar

Knibbs, L. D., L. Morawska, and S. C. Bell. 2012. The risk of airborne influenza transmission in passenger cars. Epidemiology and Infection 140 (3):474–8. doi:https://doi.org/10.1017/S0950268811000835

 PubMed Web of Science ®Google Scholar

Gao, X., J. Wei, H. Lei, P. Xu, B. J. Cowling, and Y. Li. 2016. Building ventilation as an effective disease intervention strategy in a dense indoor contact network in an ideal city. PLoS ONE 11 (9):e0162481 doi:https://doi.org/10.1371/journal.pone.0162481

 PubMed Web of Science ®Google Scholar

Riley, E. C., G. Murphy, and R. L. Riley. 1978. Airborne spread of measles in a suburban elementary school. American Journal of Epidemiology 107 (5):421–32. doi:https://doi.org/10.1093/oxfordjournals.aje.a112560

 PubMed Web of Science ®Google Scholar

Gammaitoni, L., and M. C. Nucci. 1997. Using a mathematical model to evaluate the efficacy of TB control measures. Emerging Infectious Diseases 3 (3):335–42. doi:https://doi.org/10.3201/eid0303.970310

 PubMed Web of Science ®Google Scholar

Weber, A., K. Willeke, R. Marchloni, T. Myojo, R. McKay, J. Donnelly, and F. Liebhaber. 1993. Aerosol penetration and leakae characteristics of masks used in the health care industry. American Journal of Infection Control 21 (4):167–73. doi:https://doi.org/10.1016/0196-6553(93)90027-2

 PubMed Web of Science ®Google Scholar

Davies, A., K.-A. Thompson, K. Giri, G. Kafatos, J. Walker, and A. Bennett. 2013. Testing the efficacy of homemade masks: Would they protect in an influenza pandemic? Disaster Medicine and Public Health Preparedness 7 (4):413–8. doi:https://doi.org/10.1017/dmp.2013.43

 PubMed Web of Science ®Google Scholar

Lee, S. A., S. A. Grinshpun, and T. Reponen. 2008. Respiratory performance offered by N95 respirators and surgical masks: Human subject evaluation with NaCl aerosol representing bacterial and viral particle size range. The Annals of Occupational Hygiene 52 (3):177–85. doi:https://doi.org/10.1093/annhyg/men005

 PubMed Web of Science ®Google Scholar

Xu, P., E. Kujundzic, J. Peccia, M. P. Schafer, G. Moss, M. Hernandez, and S. L. Miller. 2005. Impact of environmental factors on efficacy of upper-room air ultraviolet germicidal irradiation for inactivating airborne mycobacteria. Environmental Science & Technology 39 (24):9656–64. doi:https://doi.org/10.1021/es0504892

 PubMed Web of Science ®Google Scholar

Liao, C.-M., Y.-J. Lin, and Y.-H. Cheng. 2013. Modeling the impact of control measures on tuberculosis infection in senior care facilities. Building and Environment 59:66–75. : doi:https://doi.org/10.1016/j.buildenv.2012.08.008

 Web of Science ®Google Scholar