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Risk of transmission of airborne infection during train commute based on mathematical model



In metropolitan areas in Japan, train commute is very popular that trains are over-crowded with passengers during rush hour. The purpose of this study is to quantify public health risk related to the inhalation of airborne infectious agents in public vehicles during transportation based on a mathematical model.


The reproduction number for the influenza infection in a train (RA) was estimated using a model based on the Wells-Riley model. To estimate the influence of environmental parameters, the duration of exposure and the number of passengers were varied. If an infected person will not use a mask and all susceptible people will wear a mask, a reduction in the risk of transmission could be expected.


The estimated probability distribution of RA had a median of 2.22, and the distribution was fitted to a log-normal distribution with a geometric mean of 2.22 and a geometric standard deviation of 1.53, under the condition that there are 150 passengers, and that 13 ventilation cycles per hour, as required by law, are made. If the exposure time is less than 30 min, the risk may be low. The exposure time can increase the risk linearly. The number of passengers also increases the risk. However, RA is fairly insensitive to the number of passengers. Surgical masks are somewhat effective, whereas High-Efficiency Particulate Air (HEPA) masks are quite effective. Doubling the rate of ventilation reduces RA to almost 1.


Because it is not feasible for all passengers to wear a HEPA mask, and improvement in the ventilation seems to be an effective and feasible means of preventing influenza infection in public trains.


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Correspondence to Hiroyuki Furuya.

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Furuya, H. Risk of transmission of airborne infection during train commute based on mathematical model. Environ Health Prev Med 12, 78–83 (2007).

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Key words

  • airborne infection
  • influenza
  • train car
  • Wells-Riley model
  • enclesed space