The use of the SEIR model of compartmentalized population dynamics with an added fomite term is analysed as a means of statistically quantifying the contribution of contaminated fomites to the spread of a viral epidemic. It is shown that for normally expected lifetimes of a virus on fomites, the dynamics of the populations are nearly indistinguishable from the case without fomites. With additional information, such as the change in social contacts following a lockdown, however, it is shown that, under the assumption that the reproduction number for direct infection is proportional to the number of social contacts, the population dynamics may be used to place meaningful statistical constraints on the role of fomites that are not affected by the lockdown. The case of the Spring 2020 UK lockdown in response to COVID-19 is presented as an illustration. An upper limit is found on the transmission rate by contaminated fomites of fewer than 1 in 30 per day per infectious person (95% CL) when social contact information is taken into account. Applied to postal deliveries and food packaging, the upper limit on the contaminated fomite transmission rate corresponds to a probability below 1 in 70 (95% CL) that a contaminated fomite transmits the infection. The method presented here may be helpful for guiding health policy over the contribution of some fomites to the spread of infection in other epidemics until more complete risk assessments based on mechanistic modelling or epidemiological investigations may be completed.
Citation: Avery Meiksin. Using the SEIR model to constrain the role of contaminated fomites in spreading an epidemic: An application to COVID-19 in the UK[J]. Mathematical Biosciences and Engineering, 2022, 19(4): 3564-3590. doi: 10.3934/mbe.2022164
The use of the SEIR model of compartmentalized population dynamics with an added fomite term is analysed as a means of statistically quantifying the contribution of contaminated fomites to the spread of a viral epidemic. It is shown that for normally expected lifetimes of a virus on fomites, the dynamics of the populations are nearly indistinguishable from the case without fomites. With additional information, such as the change in social contacts following a lockdown, however, it is shown that, under the assumption that the reproduction number for direct infection is proportional to the number of social contacts, the population dynamics may be used to place meaningful statistical constraints on the role of fomites that are not affected by the lockdown. The case of the Spring 2020 UK lockdown in response to COVID-19 is presented as an illustration. An upper limit is found on the transmission rate by contaminated fomites of fewer than 1 in 30 per day per infectious person (95% CL) when social contact information is taken into account. Applied to postal deliveries and food packaging, the upper limit on the contaminated fomite transmission rate corresponds to a probability below 1 in 70 (95% CL) that a contaminated fomite transmits the infection. The method presented here may be helpful for guiding health policy over the contribution of some fomites to the spread of infection in other epidemics until more complete risk assessments based on mechanistic modelling or epidemiological investigations may be completed.
[1] | S. Boone, C. Gerba, Signifance of fomites in the spread of respiratory and enteric viral disease, Appl. Environ. Microbiol., 73 (2007), 1687–1696. https://doi.org/10.1128/AEM.02051-06 doi: 10.1128/AEM.02051-06 |
[2] | D. Goldmann, Transmission of viral respiratory infections in the home, Pediatr. Infect. Dis. J., 19 (2000), S97–102. |
[3] | J. Kutter, M. Spronken, P. Fraaij, R. Fouchier, S. Herfst, Transmission routes of respiratory viruses among humans, Curr. Opin. Virol., 28 (2018), 142–151. https://doi.org/10.1016/j.coviro.2018.01.001 doi: 10.1016/j.coviro.2018.01.001 |
[4] | N. Leung, Transmissibility and transmission of respiratory viruses, Nature Revs. Microbiol., (2021). https://doi.org/10.1038/s41579-021-00535-6 |
[5] | J. Barker, D. Stevens, S. Bloomfield, Spread and prevention of some common viral infections in community facilities and domestic homes, J. Appl. Microbiol., 91 (2001), 7–21. https://doi.org/10.1046/j.1365-2672.2001.01364.x doi: 10.1046/j.1365-2672.2001.01364.x |
[6] | G. Sze-To, Y. Yang, J. Kwan, S. Yu, C. Chao, Effects of surface material, ventilation, and human behavior on indirect contact transmission risk of respiratory infection, Risk Analys., 34 (2014), 818–830. https://doi.org/10.1111/risa.12144 doi: 10.1111/risa.12144 |
[7] | A. Kraay, M. Hayashi, N. Hernandez-Ceron, I. Spicknall, M. Eisenberg, R. Meza, et al., Fomite-mediated transmission as a sufficient pathway: a comparative analysis across three viral pathogens, BMC Infect. Dis., 18 (2018). https://doi.org/10.1186/s12879-018-3425-x doi: 10.1186/s12879-018-3425-x |
[8] | J. Otter, C. Donskey, S. Yezli, S. Douthwaite, S. Goldenberg, D. Weber, Air, surface environmental, and personal protective equipment contamination by severe acute respiratory syndrome coronavirus 2 (sars-cov-2) from a symptomatic patient, J. Hosp. Infec., 92 (2016) 235–250. https://doi.org/10.1016/j.jhin.2015.08.027 doi: 10.1016/j.jhin.2015.08.027 |
[9] | S. Ong, Y. Tan, P. Chia, et al., Air, surface environmental, and personal protective equipment contamination by severe acute respiratory syndrome coronavirus 2 (sars-cov-2) from a symptomatic patient, JAMA, 323 (2020), 1610–1612. https://doi.org/10.1001/jama.2020.3227 doi: 10.1001/jama.2020.3227 |
[10] | P. Azimi, Z. Keshavarz, J. Laurent, B. Stephens, J. Allen, Mechanistic transmission modeling of covid-19 on the diamond princess cruise ship demonstrates the importance of aerosol transmission, PNAS, 118 (2021). https://doi.org/10.1073/pnas.2015482118 |
[11] | B. Stephens, P. Azimi, M. Thoemmes, M. Heidarinejad, J. Allen, J. Gilbert, Microbial exchange via fomites and implications for human health, Curr. Poll. Reps., 5 (2019), 198–213. https://doi.org/10.1007/s40726-019-00123-6 doi: 10.1007/s40726-019-00123-6 |
[12] | S. Rushton, R. Sanderson, W. Reid, M. Shirley, J. Harris, P. Hunter, et al., Transmission routes of rare seasonal diseases: The case of norovirus infections, Phil. Trans. R. Soc. B, 374 (2019). https://doi.org/10.1098/rstb.2018.0267 |
[13] | WHO, Transmission of sars-cov-2: implications for infection prevention precautions, Scientific Brief. World Health Organization (WHO), (last accessed 25 May 2021) (2020). Available from: https://www.who.int/news-room/commentaries/detail/transmission-of-sars-cov-2-implications-for-infection-prevention-precautions |
[14] | NCIRD, Sars-cov-2 and surface (fomite) transmission for indoor community environments, CDC COVID-19 Science Briefs. National Center for Immunization and Respiratory Diseases, (NCIRD), (last accessed 25 October 2021) (2021). Available from: https://www.ncbi.nlm.nih.gov/books/NBK570437/#!po=1.11111 |
[15] | Y. Zuo, W. Uspal, T. Wei, Airborne transmission of covid-19: Aerosol dispersion, lung deposition, and virus-receptor interactions, ACS Nano., 14 (2020), 16502–16524. https://doi.org/10.1021/acsnano.0c08484 doi: 10.1021/acsnano.0c08484 |
[16] | D. Lewis, Covid-19 rarely spreads through surfaces. so why are we still deep cleaning?, Nature, 590 (2021), 26–28. https://doi.org/10.1038/d41586-021-00251-4 doi: 10.1038/d41586-021-00251-4 |
[17] | L. Morawska, D. Milton, It is time to address airborne transmission of coronavirus disease 2019 (covid-19), Clin. Infect. Dis., 71 (2020), 2311–2313. https://doi.org/10.1093/cid/ciaa939 doi: 10.1093/cid/ciaa939 |
[18] | N. van Doremalen, T. Bushmaker, D. Morris, M. G. Holbrook, A. Gamble, B. N. Williamson, et al., Aerosol and surface stability of sars-cov-2 as compared with sars-cov-1, N. Engl. J. Med., 382 (2020), 1564–1567. https://doi.org/10.1056/NEJMc2004973 doi: 10.1056/NEJMc2004973 |
[19] | F. Jiang, X.-L. Jiang, Z.-G. Wang, Z.-H. Meng, S.-F. Shao, B. Anderson, M.-J. Ma, Detection of severe acute respiratory syndrome coronavirus 2 rna on surfaces in quarantine rooms, Emerg. Infect. Dis., 26 (2020), 2162–2164. |
[20] | D. Harbourt, A. Haddow, A. Piper, H. Bloomfield, B. J. Kearney, D. Fetterer, et al., Modeling the stability of severe acute respiratory syndrome coronavirus 2 (sars-cov-2) on skin, currency, and clothing, PLoS Negl. Trop. Dis., 14 (2020), e0008831. https://doi.org/10.1371/journal.pntd.0008831 doi: 10.1371/journal.pntd.0008831 |
[21] | B. Pastorino, F. Touret, M. Gilles, X. de Lamballerie, R. Charrel, Prolonged infectivity of sars-cov-2 in fomites, Emerg. Infect. Dis., 26 (2020), 2256–2257. https://doi.org/10.3201/eid2609.201788 doi: 10.3201/eid2609.201788 |
[22] | M. Colaneri, E. Seminari, S. Novati, E. Asperges, S. Biscarini, A. Piralla, et al., Severe acute respiratory syndrome coronavirus 2 rna contamination of inanimate surfaces and virus viability in a health care emergency unit, Clin. Microbiol. Infect., 26 (2020), 1094.e1–1094.e5. https://doi.org/10.1016/j.cmi.2020.05.009 doi: 10.1016/j.cmi.2020.05.009 |
[23] | L. Al-Ansary, G. Bawazeer, E. Beller, J. Clark, J. Conly, C. Del Mar, et al., Physical interventions to interrupt or reduce the spread of respiratory viruses. part 2 - hand hygiene and other hygiene measures: Systematic review and meta-analysis, preprint, (last accessed 14 June 2021) (2020). https://doi.org/10.1101/2020.04.14.20065250 |
[24] | C. Lio, H. Cheon, C. Lei, Iek L. Lo, L. Yao, C. Lam, et al., Effectiveness of personal protective health behaviour against covid-19, BMC Public Health, 21 (2021), 827. https://doi.org/10.1186/s12889-021-10680-5 doi: 10.1186/s12889-021-10680-5 |
[25] | S. Belluco, M. Mancin, F. Marzoli, A. Bortolami, E. Mazzetto, A. Pezzuto, et al., Prevalence of sars-cov-2 rna on inanimate surfaces: a systematic review and meta-analysis, Eur. J. Epidem., (last accessed 24 September 2021) (2021). https://doi.org/10.1007/s10654-021-00784-y |
[26] | I. Onakpoya, C. Heneghan, E. Spencer, J. Brassey, A. Plüddemann, D. H. Evans, et al., Sars-cov-2 and the role of fomite transmission: a systematic review [version3; peer review: 2 approved], F1000Research, 10 (2021). https://doi.org/10.12688/f1000research.51590.3 |
[27] | E. Goldman, Sars wars: The fomites strike back, Appl. Environ. Microbiol., 87 (2021). https://doi.org/10.1128/AEM.00653-21 |
[28] | A. Pitol, T. Julian, Community transmission of sars-cov‐2 by surfaces: risks and risk reduction strategies, Environ. Sci. Technol. Lett., 8 (2021), 263–269. https://doi.org/10.1021/acs.estlett.Oc00966 doi: 10.1021/acs.estlett.Oc00966 |
[29] | A. Wilson, M. Weir, S. Bloomfield, E. Scott, K. Reynolds, Modeling covid-19 infection risks for a single hand-to-fomite scenario and potential risk reductions offered by surface disinfection, Am. J. Infec. Contr., 49 (2021), 846–848. https://doi.org/10.1016/j.ajic.2020.11.013 doi: 10.1016/j.ajic.2020.11.013 |
[30] | P. Liu, M. Yang, X. Zhao, Y. Guo, L. Wang, J. Zhang, et al., Cold-chain transportation in the frozen food industry may have caused a recurrence of covid-19 cases in destination: Successful isolation of sars-cov-2 virus from the imported frozen cod package surface, Biosaf. Health, 2 (2020), 199–201. |
[31] | W. Ji, X. Li, S. Chen, L. Ren, Transmission of sars-cov-2 via fomite, especially cold chain, should not be ignored, Proc. Natl. Acad. Sci. USA, 118 (2021). |
[32] | J. Sobolik, E. Sajewski, L.-A. Jaykus, D. Cooper, B. Lopman, A. Kraay, et al., Low risk of sars-cov-2 transmission via fomite, even in cold-chain, preprint, (last accessed 27 October 2021) (2021). https://doi.org/10.1101/2021.08.23.21262477 |
[33] | WHO, Quantitative microbial risk assessment. application for water safety management, Scientific Brief. World Health Organization (WHO), (last accessed 14 November 2021) (2016). Available from: https://apps.who.int/iris/handle/10665/246195 |
[34] | S. Flaxman, S. Mishra, A. Gandy, H. J. T. Unwin, T. A. Mellan, H. Coupland, et al., Estimating the effects of non-pharmaceutical interventions on covid-19 in europe, Nature, 584 (2020), 257–261. https://doi.org/10.1038/s41586-020-2405-7 doi: 10.1038/s41586-020-2405-7 |
[35] | A. Ault, Mail handlers used to poke holes in envelopes to battle germs and viruses, Smiths Mag. (last accessed 20 October 2021) (2020). |
[36] | A. Chang, A. Schnall, R. Law, A. C. Bronstein, J. M. Marraffa, H. A. Spiller, et al., Exposures and temporal associations with covid-19 - national poison data system, united states, January 1, 2020–march 31, 2020, CDC MMWR Morb. Mortal Wkly. Rep., 69 (2020), 496–498. https://doi.org/10.15585/mmwr.mm6916e1 doi: 10.15585/mmwr.mm6916e1 |
[37] | FSA, Guidance for consumers on coronavirus (covid-19) and food, Food Standards Agency Guidance, (last accessed 25 October 2021). Available from: https://www.gov.uk/government/publications/guidance-for-consumers-on-coronavirus-covid-19-and-food/guidance-for-consumers-on-coronavirus-covid-19-and-food |
[38] | UNICEF, Cleaning and hygiene tips to help keep the covid-19 virus out of your home, (last accessed 25 October 2021). Available from: https://www.unicef.org/romania/stories/cleaning-and-hygiene-tips-help-keep-covid-19-virus-out-your-home |
[39] | Mayoclinic, Fight coronavirus (covid-19) transmission at home, (last accessed 20 October 2021) (2021). Available from: https://www.mayoclinic.org/diseases-conditions/coronavirus/expert-answers/can-coronavirus-spread-food-water/faq-20485479 |
[40] | A. Meiksin, Dynamics of covid-19 transmission including indirect transmission mechanisms: A mathematical analysis, Epidem. Infect., 148 (2020), 1–7. |
[41] | D. Aldila, Cost-effectiveness and backward bifurcation analysis on covid-19 transmission model considering direct and indirect transmission, Commun. Math. Biol. Neurosci., 2020 (2020). https://doi.org/10.28919/cmbn/4779 |
[42] | J. David, S. Iyaniwura, M. Ward, F. Brauer, A novel approach to modelling the spatial spread of airborne diseases: An epidemic model with indirect transmission, Math. Biosci. Eng., 17 (2020), 3294–3328. https://doi.org/10.3934/mbe.2020188 doi: 10.3934/mbe.2020188 |
[43] | S. Iyaniwura, M. Rabiu, J. David, J. Kong, Assessing the impact of adherence to non-pharmaceutical interventions and indirect transmission on the dynamics of covid-19: A mathematical modelling study, Math. Biosci. Eng., 18 (2021), 8905–8932. https://doi.org/10.3934/mbe.2021439 doi: 10.3934/mbe.2021439 |
[44] | H. Zhong, W. Wang, Mathematical analysis for covid-19 resurgence in the contaminated environment, Math. Biosci. Eng., 17 (2020), 6909–6927. https://doi.org/10.3934/mbe.2020357 doi: 10.3934/mbe.2020357 |
[45] | K. Wijaya, N. Ganegoda, Y. Jayathunga, T. Götz, M. Schäfer, P. Heidrich, An epidemic model integrating direct and fomite transmission as well as household structure applied to covid-19, J. Math. Indus., 11 (2021). https://doi.org/10.1186/s13362-020-00097-x |
[46] | H. Hethcote, The basic epidemiology models: models, expressions for $r_0$, parameter estimation, and applications, in: S. Ma, Y. Xia (Eds.), Mathematical Understanding Of Infectious Disease Dynamics, Vol. 16 of Lecture Notes Series, Institute For Mathematical Sciences, National University Of Singapore, World Scientific Publishing Co. Pte. Ltd, Singapore, 2009, Ch. 1, pp. 1–62. |
[47] | N. Davies, A. Kucharski, R. Eggo, A. Gimma, W. Edmunds, Effects of non-pharmaceutical interventions on covid-19 cases, deaths, and demand for hospital services in the UK: A modelling study, Lancet Public Health 5 (2020), e375–e385. https://doi.org/10.1016/S2468-2667(20)30133-X doi: 10.1016/S2468-2667(20)30133-X |
[48] | PHAS, The infection fatality rate of covid-19 in stockholm, Tech. rep., Folkhälsomyndigheten: Public Health Agency of Sweden (PHAS), (last accessed 28 May 2021) (2020). Available from: https://www.folkhalsomyndigheten.se/publicerat-material/ |
[49] | T. Russell, J. Hellewell, C. Jarvis, K. van Zandvoort, S. Abbott, R. Ratnayake, et al., Estimating the infection and case fatality ratio for coronavirus diseases (covid-19) using age-adjusted data from the outbreak on the diamond princess cruised ship, February 2020, Euro. Serveill., 25 (2020). https://doi.org/10.2807/1560-7917.ES.2020.25.12.2000256 |
[50] | L. du Plessis, J. McCrone, A. Zarebski, V. Hill, C. Ruis, B. Gutierrez, et al., Establishment & lineage dynamics of the sars-cov-2 epidemic in the UK, Science, 371 (2021), 708–712. https://doi.org/10.1126/science.abf2946 doi: 10.1126/science.abf2946 |
[51] | C. Jarvis, K. Van Zandvoort, A. Gimma, K. Prem, CMMID COVID-19 working group, P. Klepac, et al., Quantifying the impact of physical distance measures on the transmission of covid-19 in the uk, BMC Med., 18 (2020). https://doi.org/10.1186/s12916-020-01597-8 |
[52] | DHSC/SAGE, The r value and growth rate, Department of Health and Social Care (DHSC) and Scientific Advisory Group for Emergencies (SAGE), (last accessed 15 June 2021) (2021). Available from: https://www.gov.uk/guidance/the-r-value-and-growth-rate |
[53] | ONS, Expenditure on food and non-alcoholic drinks by place of purchase: table a2, Office for National Statistics (ONS), (last accessed 11 June 2021) (2020). Available from: https://www.ons.gov.uk |
[54] | ONS, Families and households in the UK: 2020, Statistical bulletin. Office for National Statistics (ONS), (last accessed 11 June 2021) (2021). Available from: https://www.ons.gov.uk |
[55] | J. Abrahão, L. Sacchetto, I. M. Rezende, R. A. L. Rodrigues, A. P. C. Crispim, C. Moura, et al., Detection of sars-cov-2 rna on public surfaces in a densely populated urban area of brazil: A potential tool for monitoring the circulation of infected patients, Sci. Tot. Environ., 766 (2021). https://doi.org/10.1016/j.scitotenv.2020.142645 |
[56] | A. Harvey, E. Fuhrmeister, M. Cantrell, A. Pitol, J. Swarthout, J. Powers, et al., Longitudinal monitoring of sars-cov-2 rna on high-touch surfaces in a community setting, Environ. Sci. Technol. Lett., 8 (2021), 168–175. https://doi.org/10.1021/acs.estlett.0c00875 doi: 10.1021/acs.estlett.0c00875 |
[57] | E. Ince, Ordinary differential equations, Dover Publications, New York, 1956–1926. |