We developed a modelling framework to capture the key components of pathogen transmission on public transport networks. This is a general framework that could be used for a wide variety of pathogens, transport modes (including multi-modal) and public transport networks, though here we focus on COVID-19 transmission on trains. An overview of the modelling framework is provided in Fig. 4. There are four main components:
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Transit assignment engine: a transit assignment engine simulating the movement of passengers in the public transport network. For our case study, this is the train network in Sydney, Australia.
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Modelling the spread of infection: the transit disease spread model. For our COVID-19 case study, this incorporates two forms of transmission: direct (person-to-person) and fomite (person-to-surface-to-person).
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Outputs: an analytical module providing summary statistics and visualisations of results.
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Disease seeding: a community-wide transmission model that informs disease seeding (the expected number of infectious passengers on the Sydney train network).
In addition to these components, our modelling framework requires input data and specification of the scenarios of interest (such as including any non-pharmaceutical interventions being considered).
In our case study, this framework involves assigning a passenger to a train trip leg based on travel smart card data and an assigned shortest feasible path. Each leg of the trip is assigned to a transit service vehicle (in this case, a train), according to a specified capacity and current occupancy. The trains operate in accordance with a pre-defined schedule. Every time a passenger finishes their trip, the transit disease model is triggered and this passenger is assigned an exposure status (that is, whether the passenger was infected during their trip). The information about new infections is sent to the visualisation module to be displayed on a dashboard. At the end of every simulated day and at the end of the simulation horizon, the total number of new infections is calculated and reported for final evaluation. The SAfE Transport modules are further described in "Transist assignment engine"–"Seeding".
Transit assignment engine
The transit assignment engine is an agent-based simulation platform that maps trip demand to transit service supply. The transit assignment engine underpins SAfE Transport, as it provides the network of contacts between travelling passengers (that is, with whom and for how long they are in contact).
The engine depends on input data in the form of:
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trip demand (that is, trip origin, trip destination, and starting trip time for every passenger), and
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transit service supply (that is, routes and schedules of public transport services).
The full architecture is provided in the Additional file 1. The total number of trips on Sydney’s train network before COVID-19 was about 8 million per week. To account for the patronage drop during COVID-19, we assume the demand to be 10% of the total, which aligns with the real-life observations [27, 29, 30]. The supply of services did not change in Sydney due to COVID-19. Trip demand is captured by smart cards, including tap-on and tap-off data with location GPS coordinates and timestamp. This is used by the shortest path router to calculate a set of time-dependent shortest paths for each travelling passenger using the classic Dijkstra algorithm. Throughout the simulation, passengers are tracked and detailed dynamic outputs are collected for every agent, link (between two consecutive stops/stations), stop/station, service vehicle, service line, and the whole network.
Modelling the spread of infection on trains
At its core, the disease spread model on trains provides a probability of becoming infected for each susceptible passenger, based on the current and past travel of infectious passengers in the same spatial area. The model uses a number of simplifying assumptions, the most important being that we ignore any age-based effects (all agents are identical). We also assume homogeneity of mixing within the spatial area considered, including an equal distribution of passengers throughout the train. To account for our homogeneous mixing within a spatial area assumption, we use a half-carriage spatial area for our model, due to the stack structure (including upper and lower deck) of the Sydney train carriages (Waratah design).
The overall probability of a susceptible individual being infected is based on the standard probabilistic statement of being one minus the probability that they were not infected. This allows us to consider the probability of infection from each of the infectious passengers, and the surfaces on the half-carriage, separately. The transmission model uses the regression expression for the attack rate from the study by Hu et al. [19] (Fig 4 in [19], Average of all seats), both directly for the empirical person-to-person part of our transmission model, and for calibration of the mechanistic person-to-surface-to-person model. The mechanistic model is based on the transmission route model developed by Atkinson and Wein [1]. This approach models proportion of the virus shed drops to the surface, and the effective dose based on surface concentration. We then use a standard dose-response model for the probability of infection from contaminated surfaces (fomites). Further details of the transmission model are provided in the Additional file 1, along with sensitivity analyses of key parameters.
Seeding
Our primary disease spread model, as outlined in "Modelling the spread of infection on trains" only considers transmission on the public transport network (and is specifically calibrated to trains). To keep the numbers of infectious passengers travelling on trains identical across simulations for comparability, we use a deterministic compartmental model to approximate the transmission dynamics in the general community.
We use the standard susceptible-exposed-infectious-recovered progression structure, with the exposed and infectious compartments repeated to better account for the distribution of time spent in those states (see, for example, [20]). We refer to this as an “SEEIIR” model for short. We start the deterministic SEEIIR model with 2000 infectious cases, using the population of Sydney of 5.73 million in 2019 [4], and a basic reproduction number of 2.5 [6, 23, 45]. We used estimates of the proportion of the population that commutes via public transport (approximately 20% according to Census 2006, 2001 and 2016 data [2, 28]), and the proportion of commuters who use trains (approximately 50.9% [39]), to arrive at an estimate of 10% of the population using trains in Sydney. Further details are provided in the Additional file 1, including a table with the numbers used to seed infectious passengers for each of the 7 days.
Face mask wearing scenarios
The primary objective of this work was to explore the probable impacts of different face mask wearing proportions by passengers (that is, face mask coverage). How the mask wearing status of passengers effects the transit transmission model depends on whether the passenger is susceptible or infectious. The mask wearing status of infectious individuals reduces viral shedding. The mask wearing status of susceptible individuals is known to reduce the overall probability of infection [38], but does this through two separate mechanisms: (i) it explicitly effects the probability of being infected from the direct transmission component; and (ii) it effects the effective dose from the surface for the fomite transmission component.
To parameterise the viral shedding effect on those infectious passengers, we use the filtration efficacy of a two-layer cloth mask, as described in Howard et al. [18]. They discovered that two-layer cloth masks reduce infectious particle load by 88-94% and have a filtration efficacy of 80-90%. In our modelling, we use 90% as it is within both of these bounds, and reduction in infection particle load is arguably the most important aspect.
For the reduction in susceptibility, the model was calibrated using a minimisation of the sum of squared errors to achieve the reported odds ratio of 0.22 for wearing a mask [38]. There is further information on this provided in the Additional file 1.