Modeling the factors that influence exposure to SARS‐CoV‐2 on a subway train carriage

Abstract We propose the Transmission of Virus in Carriages (TVC) model, a computational model which simulates the potential exposure to SARS‐CoV‐2 for passengers traveling in a subway rail system train. This model considers exposure through three different routes: fomites via contact with contaminated surfaces; close‐range exposure, which accounts for aerosol and droplet transmission within 2 m of the infectious source; and airborne exposure via small aerosols which does not rely on being within 2 m distance from the infectious source. Simulations are based on typical subway parameters and the aim of the study is to consider the relative effect of environmental and behavioral factors including prevalence of the virus in the population, number of people traveling, ventilation rate, and mask wearing as well as the effect of model assumptions such as emission rates. Results simulate generally low exposures in most of the scenarios considered, especially under low virus prevalence. Social distancing through reduced loading and high mask‐wearing adherence is predicted to have a noticeable effect on reducing exposure through all routes. The highest predicted doses happen through close‐range exposure, while the fomite route cannot be neglected; exposure through both routes relies on infrequent events involving relatively few individuals. Simulated exposure through the airborne route is more homogeneous across passengers, but is generally lower due to the typically short duration of the trips, mask wearing, and the high ventilation rate within the carriage. The infection risk resulting from exposure is challenging to estimate as it will be influenced by factors such as virus variant and vaccination rates.

excess passengers are moved to the 1-2m region. 48 6. If the number of passengers in the 1-2m region is greater than T 12 then passengers are moved out 49 of the region into the rest of the carriage. Passengers moved into this region within the previous 50 step are chosen last from the list of passengers eligible to be moved out of the region. Here, we give an overview of the method used in order to adjust the surface area and available 53 volume in 0-1m and 1-2m of the infectious passenger to account for possible positions of this passenger 54 within the carriage; see Figure 1 which has been generated from available information in [1]. To begin, 55 a rectangular grid is generated with the same dimensions as the width and length of the carriage. At 56 each grid point, a random sample is generated from a uniform distribution for a 1m disc and for an 57 annulus between 1m and 2m radii, see Figure 2. Then, the number of points that lie inside the carriage 58 is counted and divided by the total number of points to yield a proportion of the disc/annulus that lies 59 inside the carriage at a given point within the carriage. The proportion of the disc and the proportion 60 of the annulus at a given point will be linked ( Figure 1) and it is therefore necessary to consider what 61 the proportion at 1-2m is, given the proportion at 0-1m. The array of proportions for 0-1m is then sorted from smallest to largest with the associated array 63 of 1-2m values sorted according to the 0-1m value at that carriage position. The 0-1m values are then 64 binned, the number of values in each bin counted and divided by the total number of points to generate a probability of the 0-1m value lying in that bin. An array of bin midpoints is also generated. We then generate a sample of 0-1m carriage proportions (from the bin midpoints) with a weighting dictated by 67 the probability of a value lying in that bin.

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A probability distribution for the 1-2m values is then generated as follows. The 1-2m values for 69 a given 0-1m bin are binned using the same bin edges and widths as the 0-1m bins. As before, the

Surface area within the carriage 85
To calculate the fraction of deposited droplets that deposits onto mucosal membranes, it is required 86 to obtain an estimate of the surface area (SA) within the carriage as a whole and the region of the 87 carriage within 2m of an infectious passenger.

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The total surface area within the carriage has the following components: the carriage floor surface 89 area, the ceiling surface area, the four walls areas, the number of internal surfaces multiplied by their 90 surface area (see Table 2 in this Supplementary Material), the number of passengers on board at any 91 given time multiplied by their surface area (see Table 2   There is no current consensus on which droplet size distribution best fits human behaviour for the 101 activities which are of most interest (coughing, speaking, breathing). As such, choice of droplet size 102 distribution varies significantly within the literature. One common choice is to use the data given by following sum of lognormal distributions: with the parameters in Table 1.

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Parameter Coughing Speaking Breathing B mode By assuming an homogeneous viral load per unit volume across droplet sizes, and for a particular 127 droplet size j = 1, . . . , M , the volume concentration [m 3 · m −3 ] is then calculated using the formula 128 dC vol j = 4 3 · π · x j 2 3 · dCn j , and the source term [P F U · s −1 ] for coughing is found via between 0 and 100, with 100 denoting all passengers wearing masks and 0 indicating that no passengers 135 are wearing masks. The impact of wearing a mask for infectious individuals is a reduction in their 136 release of small aerosol and droplets. In particular, it is assumed that masks block all large droplets, 137 while a 50% filtration efficacy is assumed for small aerosols [9, 10]. This filtration efficacy is also applied 138 to reduce the exposure of susceptible passengers who are wearing a mask.

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In Figures 4 and 5, we explore the impact that the interaction between the droplet model under   is determined following the approach of [7]. In particular, we define an evaporation time where β [s · m −2 ] is a fitting parameter and r 2 0 is the wet droplet radius squared. We also define a travel  (either within 1m or 1-2m away). We then have the following scenarios for a droplet of a given wet for the evaporated droplets radius. As discussed above, it is this radius which is used within the TVC 186 model wherever calculations of deposition, filtration or protection of exposed individuals by masks 187 require the use of a droplet radius, with the exception of source reduction for infected individuals due 188 to mask wearing.