No Access
Published Online: 13 April 2021
Accepted: March 2021
Chaos 31, 043115 (2021); https://doi.org/10.1063/5.0041993
The COVID-19 pandemic has laid bare the importance of non-pharmaceutical interventions in the containment of airborne infectious diseases. Social distancing and mask-wearing have been found to contain COVID-19 spreading across a number of observational studies, but a precise understanding of their combined effectiveness is lacking. An underdeveloped area of research entails the quantification of the specific role of each of these measures when they are differentially adopted by the population. Pursuing this research allows for answering several pressing questions like: how many people should follow public health measures for them to be effective for everybody? Is it sufficient to practice social distancing only or just wear a mask? Here, we make a first step in this direction, by establishing a susceptible–exposed–infected–removed epidemic model on a temporal network, evolving according to the activity-driven paradigm. Through analytical and numerical efforts, we study epidemic spreading as a function of the proportion of the population following public health measures, the extent of social distancing, and the efficacy of masks in protecting the wearer and others. Our model demonstrates that social distancing and mask-wearing can be effective in preventing COVID-19 outbreaks if adherence to both measures involves a substantial fraction of the population.
This work was supported by the National Science Foundation (NSF) (Nos. CMMI-1561134 and CMMI-2027990) and by Compagnia di San Paolo.
  1. 1. J. B. Nuzzo, L. Mullen, M. Snyder, A. Cicero, and T. V. Inglesby, Preparedness for a High Impact Respiratory Pathogen Pandemic (The Johns Hopkins Center for Health Security, 2019), p. 84. Google Scholar
  2. 2. Centers for Disease Control and Prevention, “1918 pandemic (H1N1 virus),” see https://www.cdc.gov/flu/pandemic-resources/1918-pandemic-h1n1.html (last accessed March 11, 2020). Google Scholar
  3. 3. R. D. Smith, “Responding to global infectious disease outbreaks: Lessons from SARS on the role of risk perception, communication and management,” Soc. Sci. Med. 63, 3113–3123 (2006). https://doi.org/10.1016/j.socscimed.2006.08.004, Google ScholarCrossref
  4. 4. R. J. de Groot, S. C. Baker, R. S. Baric, C. S. Brown, and C. Drosten, Enjuanes, “Commentary: Middle East respiratory syndrome coronavirus (MERS-CoV): Announcement of the coronavirus study group,” J. Virol. 87, 7790–7792 (2013). https://doi.org/10.1128/JVI.01244-13, Google ScholarCrossref
  5. 5. Centers for Disease Control and Prevention, “Summary of probable SARS cases with onset of illness,” see https://www.who.int/health-topics/severe-acute-respiratory-syndrome (last accessed March 11, 2020). Google Scholar
  6. 6. World Health Organization, “Eastern Mediterranean Region,” see http://www.emro.who.int/health-topics/mers-cov/mers-outbreaks.html (last accessed March 11, 2020). Google Scholar
  7. 7. World Health Organization, “WHO coronavirus disease (COVID-19) dashboard,” see https://COVID19.who.int (last accessed March 11, 2020). Google Scholar
  8. 8. R. Zhang, Y. Li, A. L. Zhang, Y. Wang, and M. J. Molina, “Identifying airborne transmission as the dominant route for the spread of COVID-19,” Proc. Natl. Acad. Sci. U.S.A. 117, 14857–14863 (2020). https://doi.org/10.1073/pnas.2009637117, Google ScholarCrossref
  9. 9. E. L. Anderson, P. Turnham, J. R. Griffin, and C. C. Clarke, “Consideration of the aerosol transmission for COVID-19 and public health,” Risk Anal. 40, 902–907 (2020). https://doi.org/10.1111/risa.13500, Google ScholarCrossref
  10. 10. J. Wang and G. Du, “COVID-19 may transmit through aerosol,” Ir. J. Med. Sci. 189, 1143 (2020). https://doi.org/10.1007/s11845-020-02218-2, Google ScholarCrossref
  11. 11. D. K. Chu, E. A. Akl, S. Duda, K. Solo, S. Yaacoub, H. J. Schünemann, D. K. Chu, and E. A. Akl, “Physical distancing, face masks, and eye protection to prevent person-to-person transmission of SARS-CoV-2 and COVID-19: A systematic review and meta-analysis,” Lancet 395, 1973–1987 (2020). https://doi.org/10.1016/S0140-6736(20)31142-9, Google ScholarCrossref
  12. 12. E. Caroppo, P. De Lellis, I. Lega, A. Candelori, D. Pedacchia, A. Pellegrini, R. Sonnino, V. Venturiello, M. Ruiz Marìn, and M. Porfiri, “Unequal effects of the national lockdown on mental and social health in Italy,” Ann. Istituto Super. Sanità 56, 497–501 (2020). https://doi.org/10.4415/ANN_20_04_13, Google ScholarCrossref
  13. 13. S. K. Brooks, R. K. Webster, L. E. Smith, L. Woodland, S. Wessely, N. Greenberg, and G. J. Rubin, “The psychological impact of quarantine and how to reduce it: Rapid review of the evidence,” Lancet 395, 912–920 (2020). https://doi.org/10.1016/S0140-6736(20)30460-8, Google ScholarCrossref
  14. 14. I. F. Tso and S. Park, “Alarming levels of psychiatric symptoms and the role of loneliness during the COVID-19 epidemic: A case study of Hong Kong,” Psychiatry Res. 293, 113423 (2020). https://doi.org/10.1016/j.psychres.2020.113423, Google ScholarCrossref
  15. 15. L. Matrajt and T. Leung, “Evaluating the effectiveness of social distancing interventions to delay or flatten the epidemic curve of coronavirus disease,” Emerging Infect. Dis. 26, 1740–1748 (2020). https://doi.org/10.3201/eid2608.201093, Google ScholarCrossref
  16. 16. A. D. Wiese, J. Everson, and C. G. Grijalva, “Social distancing measures: Evidence of interruption of seasonal influenza activity and early lessons of the SARS-CoV-2 pandemic,” Clin. Infect. Diseases 2020, ciaa834. https://doi.org/10.1093/cid/ciaa834 , Google ScholarCrossref
  17. 17. S. J. Olsen, E. Azziz-Baumgartner, A. P. Budd, L. Brammer, S. Sullivan, R. F. Pineda, C. Cohen, and A. M. Fry, “Decreased influenza activity during the COVID-19 pandemic—United States, Australia, Chile, and South Africa, 2020,” Morbidity Mortality Weekly Rep. 69, 1305–1309 (2020). https://doi.org/10.15585/mmwr.mm6937a6, Google ScholarCrossref
  18. 18. E. Estrada, “COVID-19 and SARS-CoV-2. Modeling the present, looking at the future,” Phys. Rep. 869, 1–51 (2020). https://doi.org/10.1016/j.physrep.2020.07.005, Google ScholarCrossref
  19. 19. F. Parino, L. Zino, M. Porfiri, and A. Rizzo, “Modelling and predicting the effect of social distancing and travel restrictions on COVID-19 spreading,” J. R. Soc. Interface 18, 20200875 (2021). https://doi.org/10.1098/rsif.2020.0875, Google ScholarCrossref
  20. 20. M. Mancastroppa, R. Burioni, V. Colizza, and A. Vezzani, “Active and inactive quarantine in epidemic spreading on adaptive activity-driven networks,” Phys. Rev. E 102, 020301(R) (2020). https://doi.org/10.1103/PhysRevE.102.020301, Google ScholarCrossref
  21. 21. C. N. Ngonghala, E. Iboi, S. Eikenberry, M. Scotch, C. R. MacIntyre, M. H. Bonds, and A. B. Gumel, “Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel coronavirus,” Math. Biosci. 325, 108364 (2020). https://doi.org/10.1016/j.mbs.2020.108364, Google ScholarCrossref
  22. 22. A. Aleta, D. Martín-Corral, A. Pastore y Piontti, M. Ajelli, M. Litvinova, M. Chinazzi, N. E. Dean, M. E. Halloran, I. M. Longini, S. Merler, A. Pentland, A. Vespignani, E. Moro, and Y. Moreno, “Modelling the impact of testing, contact tracing and household quarantine on second waves of COVID-19,” Nature Human Behav. 4, 964 (2020). https://doi.org/10.1038/s41562-020-0931-9, Google ScholarCrossref
  23. 23. P. C. Silva, P. V. Batista, H. S. Lima, M. A. Alves, F. G. Guimarães, and R. C. Silva, “COVID-ABS: An agent-based model of COVID-19 epidemic to simulate health and economic effects of social distancing interventions,” Chaos, Solitons Fractals 139, 110088 (2020). https://doi.org/10.1016/j.chaos.2020.110088, Google ScholarCrossref
  24. 24. Centers for Disease Control and Prevention, “CDC calls on Americans to wear masks to prevent COVID-19 spread,” see https://www.cdc.gov/media/releases/2020/p0714-americans-to-wear-masks.html (last accessed March 11, 2020). Google Scholar
  25. 25. N. H. Leung, D. K. Chu, E. Y. Shiu, K. H. Chan, and J. J. M. Hau, “Respiratory virus shedding in exhaled breath and efficacy of face masks,” Nat. Med. 26, 676–680 (2020). https://doi.org/10.1038/s41591-020-0843-2, Google ScholarCrossref
  26. 26. A. Konda, A. Prakash, G. A. Moss, M. Schmoldt, G. D. Grant, and S. Guha, “Aerosol filtration efficiency of common fabrics used in respiratory cloth masks,” ACS Nano 14, 6339–6347 (2020). https://doi.org/10.1021/acsnano.0c03252, Google ScholarCrossref
  27. 27. M. Gandhi, C. Beyrer, and E. Goosby, “Masks do more than protect others during COVID-19: Reducing the inoculum of SARS-CoV-2 to protect the wearer,” J. Gen. Intern. Med. 35, 3063 (2020). https://doi.org/10.1007/s11606-020-06067-8, Google ScholarCrossref
  28. 28. W. Lyu and G. L. Wehby, “Community use of face masks and COVID-19: Evidence from a natural experiment of state mandates in the US,” Health Aff. 39, 1419–1425 (2020). https://doi.org/10.1377/hlthaff.2020.00818, Google ScholarCrossref
  29. 29. R. O. J. H. Stutt, R. Retkute, M. Bradley, C. A. Gilligan, and J. Colvin, “A modelling framework to assess the likely effectiveness of facemasks in combination with ‘lock-down’ in managing the COVID-19 pandemic,” Proc. R. Soc. Lond. A. Math. Phys. Sci. 476, 20200376 (2020). https://doi.org/10.1098/rspa.2020.0376, Google ScholarCrossref
  30. 30. D. Kai, G.-P. Goldstein, A. Morgunov, V. Nangalia, and A. Rotkirch, “Universal masking is urgent in the COVID-19 pandemic: SEIR and agent based models, empirical validation, policy recommendations,” arXiv:2004.13553 (2020). Google Scholar
  31. 31. D. N. Fisman, A. L. Greer, and A. R. Tuite, “Bidirectional impact of imperfect mask use on reproduction number of COVID-19: A next generation matrix approach,” Infect. Disease Model. 5, 405–408 (2020). https://doi.org/10.1016/j.idm.2020.06.004, Google ScholarCrossref
  32. 32. Y. Tian, A. Sridhar, O. Yagan, and H. V. Poor, “Analysis of the impact of mask-wearing in viral spread: Implications for COVID-19,” arXiv:2011.04208 (2020). Google Scholar
  33. 33. N. Perra, B. Gonçalves, R. Pastor-Satorras, and A. Vespignani, “Activity driven modeling of time varying networks,” Sci. Rep. 2, 2045–2322 (2012). https://doi.org/10.1038/srep00469, Google ScholarCrossref
  34. 34. S. Liu, N. Perra, M. Karsai, and A. Vespignani, “Controlling contagion processes in activity driven networks,” Phys. Rev. Lett. 112, 118702 (2014). https://doi.org/10.1103/PhysRevLett.112.118702, Google ScholarCrossref
  35. 35. A. Rizzo, M. Frasca, and M. Porfiri, “Effect of individual behavior on epidemic spreading in activity-driven networks,” Phys. Rev. E 90, 042801 (2014). https://doi.org/10.1103/PhysRevE.90.042801, Google ScholarCrossref
  36. 36. A. Rizzo, B. Pedalino, and M. Porfiri, “A network model for Ebola spreading,” J. Theor. Biol. 394, 212–222 (2016). https://doi.org/10.1016/j.jtbi.2016.01.015, Google ScholarCrossref
  37. 37. A. Rizzo and M. Porfiri, “Innovation diffusion on time-varying activity driven networks,” Eur. Phys. J. B 89, 1–8 (2016). https://doi.org/10.1140/epjb/e2015-60933-3, Google ScholarCrossref
  38. 38. L. Zino, A. Rizzo, and M. Porfiri, “Consensus over activity-driven networks,” IEEE Trans. Control Netw. Syst. 7, 866–877 (2020). https://doi.org/10.1109/TCNS.2019.2949387, Google ScholarCrossref
  39. 39. I. Pozzana, K. Sun, and N. Perra, “Epidemic spreading on activity-driven networks with attractiveness,” Phys. Rev. E 96, 042310 (2017). https://doi.org/10.1103/PhysRevE.96.042310, Google ScholarCrossref
  40. 40. A. L. Barabási, “The origin of bursts and heavy tails in human dynamics,” Nature 435, 1476–4687 (2005). https://doi.org/10.1038/nature03459, Google ScholarCrossref
  41. 41. H.-H. Jo, M. Karsai, J. Kertész, and K. Kaski, “Circadian pattern and burstiness in mobile phone communication,” New J. Phys. 14, 013055 (2012). https://doi.org/10.1088/1367-2630/14/1/013055, Google ScholarCrossref
  42. 42. Institute for Health Metrics and Evaluation (IHME), “COVID-19 projections,” see https://COVID19.healthdata.org/projections (last accessed March 11, 2020). Google Scholar
  43. 43. L. Peeples, “Face masks: What the data say,” Nature 586, 186 (2020). https://doi.org/10.1038/d41586-020-02801-8, Google ScholarCrossref
  44. 44. J. Howard, A. Huang, Z. Li, and A. Rimoin, “Face masks against COVID-19: An evidence review,” Proc. Natl. Acad. Sci. U.S.A. 118(4), e2014564118 (2021). https://doi.org/10.1073/pnas.2014564118, Google ScholarCrossref
  45. 45. J. Yan, S. Guha, P. Hariharan, and M. Myers, “Modeling the effectiveness of respiratory protective devices in reducing influenza outbreak,” Risk Anal. 39, 647–661 (2019). https://doi.org/10.1111/risa.13181, Google ScholarCrossref
  46. 46. M. J. Hendrix, C. Walde, K. Findley, and R. Trotman, “Absence of apparent transmission of SARS-CoV-2 from two stylists after exposure at a hair salon with a universal face covering policy in Springfield, Missouri, May 2020,” Morbidity Mortality Weekly Rep. 69, 930 (2020). https://doi.org/10.15585/mmwr.mm6928e2, Google ScholarCrossref
  47. 47. The reproduction number is the number of secondary cases in an entirely susceptible population from a single infected node. Google Scholar
  48. 48. B. Rahman, E. Sadraddin, and A. Porreca, “The basic reproduction number of SARS-CoV-2 in Wuhan is about to die out, how about the rest of the world?” Rev. Med. Virol. 30, e2111 (2020). https://doi.org/10.1002/rmv.2111, Google ScholarCrossref
  49. 49. The New York Times, “COVID-19 data,” see https://github.com/nytimes/COVID-19-data (last accessed March 11, 2020). Google Scholar
  50. 50. L. Zino, A. Rizzo, and M. Porfiri, “Modeling memory effects in activity-driven networks,” SIAM J. Appl. Dyn. Syst. 17, 2830–2854 (2018). https://doi.org/10.1137/18M1171485, Google ScholarCrossref
  51. 51. A. Truszkowska, B. Behring, J. Hasanyan, L. Zino, S. Butail, E. Caroppo, Z.-P. Jiang, A. Rizzo, and M. Porfiri, “High-resolution agent-based modeling of COVID-19 spreading in a small town,” Adv. Theory Simulat. 4(3), 2000277 (2021). https://doi.org/10.1002/adts.202000277, Google ScholarCrossref
  52. 52. J. A. Weill, M. Stigler, O. Deschenes, and M. R. Springborn, “Social distancing responses to COVID-19 emergency declarations strongly differentiated by income,” Proc. Natl. Acad. Sci. U.S.A. 117, 19658–19660 (2020). https://doi.org/10.1073/pnas.2009412117, Google ScholarCrossref
  1. © 2021 Author(s). Published under license by AIP Publishing.