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Influence of asymptomatic infections for the effectiveness of facemasks during pandemic influenza

1 School of Science, Beijing University of Civil Engineering and Architecture, Beijing 102616, P.R. China
2 Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA

Special Issues: Mathematical Modeling to Solve the Problems in Life Sciences

In this paper, the SEIR model is generalized by introducing an asymptomatic class to quantify the influence of wearing N95 facemasks in reducing the spread of influenza H1N1. What's more, we explain the control reproduction number $\mathcal R_c$ according to the biological meaning reasonably. Without any intervention, the basic reproduction number $\mathcal R_0= 1.83$ and there will be a large outbreak of infectious diseases. If N95 facemasks are 50\% effective in reducing susceptibility and infectivity, 50\% of population wear them on the first day, the basic reproduction number will be decreased from 1.83 to 1.17 and the final size reduced from 73\% to 2\%.
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Keywords pandemic influenza; facemasks; asymptomatic class; the final epidemic size

Citation: Jing’an Cui, Ya’nan Zhang, Zhilan Feng, Songbai Guo, Yan Zhang. Influence of asymptomatic infections for the effectiveness of facemasks during pandemic influenza. Mathematical Biosciences and Engineering, 2019, 16(5): 3936-3946. doi: 10.3934/mbe.2019194


  • 1. T. C. Germann, K. Kai, I. M. Longini, et al., Mitigation strategies for pandemic influenza in the United States, P. Natl. Acad. Sci. USA, 103 (2006), 5935–5940.
  • 2. S. M. Tracht, S. Y. Valle and J. M. Hyman, Mathematical modeling of the effectiveness of facemasks in reducing the spread of novel influenza A (H1N1), Plos One, 5 (2010), e9018.
  • 3. A. Aiello, G. Murray, V. Murray, et al., Mask use, hand hygiene, and seasonal influenza like illness among young adults: a randomized intervention trial, J. Infect. Dis., 201 (2010), 491–498.
  • 4. S. A. Lee, S. A. Grinshpun and T. Reponen, Respiratory performance offered by N95 respi-rators and surgical masks: human subject evaluation with NaCl aerosol representing bacterial and viral particle size range, Ann. Occup. Hyg., 52 (2008), 177–185.
  • 5. J. Cui, Y. Zhang and Z. Feng, Influence of non-homogeneous mixing on final epidemic size in a meta-population model, J. Biol. Dynam., (2018), DOI: 10.1080/17513758.2018.1484186.
  • 6. S. M. Tracht, S. Y. Valle and B. K. Edwards, Economic analysis of the use of facemasks during pandemic (H1N1) 2009, J. Theor. Biol., 300, (2012), 161–172.
  • 7. T. Chen, S. Chen, Z. Xie, et al., Simulated effectiveness of control countermeasures for influenza outbreaks based on different asymptomatic infections and transmissibility, China Trop. Med., 17 (2017), 470–476. (in Chinese)
  • 8. J. Lee, J. Kim and H. D. Kwon, Optimal control of an influenza model with seasonal forcing and age-dependent transmission rates, J. Theor. Biol., 317 (2013), 310–320.
  • 9. Centers for Disease Control and Prevention, Interim guidance on infection control measures for 2009 H1N1 influenza in healthcare settings, including protection of healthcare personnel, Miss. RN, 71 (2009), 13–18.
  • 10. R. Liu, R. Ka-kit Leung, T. Chen, et al., The effectiveness of age-specific isolation policies on epidemics of influenza A (H1N1) in a large city in Central South China, Plos One, 10 (2015), e0132588.
  • 11. J. K. Taubenberger and D. M. Morens, 1918 Influenza: the mother of all pandemics, Emerg. Infect. Dis., 12 (2006), 15–22.
  • 12. N. Zhong, Y. Li, Z. Yang, et al., Chinese guidelines for diagnosis and treatment of influenza (2011), J. Thorac. Dis., 3 (2011), 274–289.
  • 13. P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48.
  • 14. L. I. Jr, A. Nizam, S. Xu, et al., Containing pandemic influenza at the source, Science, 309 (2005), 1083–1087.
  • 15. J. W. Tang, T. J. Liebner, B. A. Craven, et al., A schlieren optical study of the human cough with and without wearing masks for aerosol infection control, J. R. Soc. Interface, 6 (2009), S727– S736.


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