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Abstract: The COVID-19 pandemic has affected communities worldwide. The metro system, an essential means of public transportation in many cities, is particularly vulnerable to the spread of the virus due to its limited space and complex passenger flow structure. As the basis of quick and effective management decision-making, it is very important bu...
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... study considers a bi-directional metro line system consisting of |N| stations, as illustrated in Fig. 1. Each station is indexed by i ∈ N = {1, 2, ...i, ..., |N|}, where N represents the set of stations. For simplicity, each station is assumed to have one hall and platform, and passengers move through the hall and wait at the platform for the service trains. Once they reach their destination, they pass through the platform and hall again ...
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... framework of the QEM is depicted in Fig. 6. The figure is inspired by Fig.1 in Qian and Ukkusuri (2021). The model requires three inputs: metro system network, commuting data, and disease parameters of interest. ...
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... us consider a bi-directional metro line with six stations: A, B, C, D, E, and F, where the down-direction (u = 1) is defined as "A to F." The travel demand for the 30 peak-hour OD pairs along the metro line is recorded in Eq. 64 and is represented by an alluvial flow diagram in Fig. 10. This diagram depicts the relative proportion of travellers (width of the ribbon) who board at one station and leave at another. The observation shows that stations B and D have relatively high boarding passenger ...
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... obtaining real data on the changes in the status of individuals after a commute is difficult, we validate the accuracy of the QEM and MEM through an agent-based simulation. The simulation software, Anylogic, is used and both pedestrians and trains are modelled as agents. The 3D simulation diagram of a station in the small-scale case is shown in Fig. 11. The assumption is made that the pedestrian agents carrying the virus (with the red aperture in Fig. 11) can effectively expose susceptible agents within a 2.5 m distance, and the other parameter settings are kept consistent with the small case scenario. The visualization of the agent-based simulation can be found in Supplemental ...
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... the accuracy of the QEM and MEM through an agent-based simulation. The simulation software, Anylogic, is used and both pedestrians and trains are modelled as agents. The 3D simulation diagram of a station in the small-scale case is shown in Fig. 11. The assumption is made that the pedestrian agents carrying the virus (with the red aperture in Fig. 11) can effectively expose susceptible agents within a 2.5 m distance, and the other parameter settings are kept consistent with the small case scenario. The visualization of the agent-based simulation can be found in Supplemental Material 1. For infectious disease dynamics, we divide the population into five statuses. However, we find ...
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... of exposed individuals, so we only consider the number of newly exposed travellers (E) in our analysis. We collect the simulation data on the total number of newly exposed travellers over time, and we get the TNNET mentioned earlier at the last moment of the simulated time. Then the results calculated by QEM and MEM are contrasted and shown in Fig. ...
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... (R-Squared). Our results reveal that QEM had a significantly better R Squared (0.945), indicating a much stronger interpretive effect, while MEM had a very poor R-Squared (0.374), indicating a large deviation. This finding demonstrates the potential for QEM to be a valuable tool in predicting and controlling the spread of infectious diseases. Fig. 13 illustrates the difference between QEM and MEM at the overall system level. Specifically, the two solid lines (left axis) depict the number of all passengers inside the system over time. The MEM assumes a constant walking velocity and disregards randomness and state-dependence. This results in faster system service for passengers and a ...
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... of individuals inside the system. Contrarily, the QEM takes into account the system's stochastic nature, the spillback among facilities (trains, platforms, and halls), and the state-dependence of service rates in facilities. This leads to longer times spent in the system, particularly during periods of congestion. Two dotted lines (right axis) in Fig. 13 explain the number of newly exposed individuals that are inside the system at each timestamp. The travellers counted in Fig. 13 only include the individuals currently inside the metro system, and individuals leaving the metro system are not considered in the subsequent timestamp. Therefore, the results presented in this figure differ ...
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... (trains, platforms, and halls), and the state-dependence of service rates in facilities. This leads to longer times spent in the system, particularly during periods of congestion. Two dotted lines (right axis) in Fig. 13 explain the number of newly exposed individuals that are inside the system at each timestamp. The travellers counted in Fig. 13 only include the individuals currently inside the metro system, and individuals leaving the metro system are not considered in the subsequent timestamp. Therefore, the results presented in this figure differ from those in Section 6.1.2. For MEM, the peak of the number of newly exposed travellers appears 100 timestamps later than the ...
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... since QEM fully considers the close contact of passengers while queuing in the station, the number of newly exposed people in the system even increases when passengers leave. This suggests that the number of newly exposed travellers generated during queuing in the system is greater than the number of newly exposed travellers who leave the system. Fig. 14 illustrates the difference between QEM and MEM at the station level. It further emphasizes the effect of queues on disease transmission. An interesting observation from Fig. 14 is that at stations B and D, the number of Compared with QEM, MEM ignores the nonlinear stochastic effect of congestion and overestimates the service ...
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... suggests that the number of newly exposed travellers generated during queuing in the system is greater than the number of newly exposed travellers who leave the system. Fig. 14 illustrates the difference between QEM and MEM at the station level. It further emphasizes the effect of queues on disease transmission. An interesting observation from Fig. 14 is that at stations B and D, the number of Compared with QEM, MEM ignores the nonlinear stochastic effect of congestion and overestimates the service efficiency. Consequently, MEM takes an optimistic view of the transmission intensity of infectious diseases. Another unexpected finding is that station C (a low-demand station between two ...
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... relationship between the TNNET and travel demand is further analyzed in Fig. 15. Concretely speaking, we vary the traffic demand from 50% to 150% of the base travel ...
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... computational efficiency of the proposed QEM is visualized in Fig. 16. We compare the run times of QEM and MEM in three travel demand scenarios. The results show that although the calculation time of QEM is slightly longer than that of MEM, both are within 1 s and are not affected by the number of passengers. This highlights the computational efficiency of the proposed QEM, making it suitable for solving ...
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... evaluate the spread of the epidemic at each station, we track the number of newly exposed travellers over time inside each hall and platform. The results are depicted in Fig. 17, where the station of Tianfu Square (TFS), located in the central business district, is particularly noticeable. Tianfu Square station has the most significant number of exposed passengers and is the only station with congestion, bringing the number of newly exposed people in the hall to more than 500 (as Fig. 17 a)), and platform to ...
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... The results are depicted in Fig. 17, where the station of Tianfu Square (TFS), located in the central business district, is particularly noticeable. Tianfu Square station has the most significant number of exposed passengers and is the only station with congestion, bringing the number of newly exposed people in the hall to more than 500 (as Fig. 17 a)), and platform to more than 350 (as Fig. 17 b)) at the end of the ...
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... the station of Tianfu Square (TFS), located in the central business district, is particularly noticeable. Tianfu Square station has the most significant number of exposed passengers and is the only station with congestion, bringing the number of newly exposed people in the hall to more than 500 (as Fig. 17 a)), and platform to more than 350 (as Fig. 17 b)) at the end of the ...
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... proportion. To verify this idea, we vary the allowed entering proportion under three levels of travel demands and observe the change in the TNNET (including the accumulated number of newly exposed travellers that queue outside the station). Suppose that the infectivity outside is half that inside the system, and then the result of QEM is shown in Fig. 18. Observations show that, under medium travel demand (n = 1), increasing the allowed entering proportion (up to 0.76) leads to an increase in inside system transmission of infectious diseases. But it also provides greater relief to outside transmission, resulting in a decline in the TNNET curve. However, if the allowed entering ...
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... the results obtained with the MEM (as depicted in Fig. 19) show a continuous decline in the TNNET curve as the allowed entering proportion increases. In MEM, the nonlinear stochastic effect of the congestion propagation within the metro system is ignored and thus the contagion inside system is greatly underestimated. Despite controlling the allowed entering proportion has a little bit of ...
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... the commuting time of passengers. Conversely, too short dwell time causes passengers who should be boarding trains to stay on the platform. Both of them increase the risk of infection. To analyze the control effects, we vary the train dwell time under three levels of travel demands and measured the TNNET. The results of the QEM are shown in Fig. 21. The results show that under medium travel demand (n = 1), the TNNET curve falls very slowly as the train dwell time increases from 20 seconds to 38 seconds. But when it is over 38 seconds, the TNNET spikes. The TNNET curves exhibit a similar trend under low, medium, and high travel demands, with some fluctuations. The optimal dwell ...
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