Multi-scale risk assessment and mitigations comparison for COVID-19 in urban public transport: A combined field measurement and modeling approach

Abstract

The outbreak of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic has caused an unparalleled disruption to daily life. Given that COVID-19 primarily spreads in densely populated indoor areas, urban public transport (UPT) systems pose significant risks. This study presents an analysis of the air change rate in buses, subways, and high speed trains based on measured CO₂ concentrations and passenger behaviors. The resulting values were used as inputs for an infection risk assessment model, which was used to quantitatively evaluate the effects of various factors, including ventilation rates, respiratory activities, and viral variants, on the infection risk. The findings demonstrate that ventilation has a negligible impact on reducing average risks (less than 10.0%) for short-range scales, but can result in a reduction of average risks by 32.1%–57.4% for room scales. When all passengers wear masks, the average risk reduction ranges from 4.5-folds to 7.5-folds. Based on our analysis, the average total reproduction numbers (R) of subways are 1.4-folds higher than buses, and 2-folds higher than high speed trains. Additionally, it is important to note that the Omicron variant may result in a much higher R value, estimated to be approximately 4.9-folds higher than the Delta variant. To reduce disease transmission, it is important to keep the R value below 1. Thus, two indices have been proposed: time-scale based exposure thresholds and spatial-scale based upper limit warnings. Mask wearing provides the greatest protection against infection in the face of long exposure duration to the omicron epidemic.

Nomenclature

$ACH$

Air change rate per hour (h⁻¹)

$B{R}_i$

exhalation rate of an index case (m³ h⁻¹)

$B{R}_s$

exhalation rate of susceptible individuals (m³ h⁻¹)

$C_r$

background quanta concentration (quanta m⁻³)

$C_o$

quanta concentration released by an infector (quanta m⁻³)

$C_{ro}$

initial background quanta concentration (quanta m⁻³)

$\bar{C}$

average CO₂ concentrations during the calculation period (ppm)

$C_a$

fraction of CO₂ contained in the exhaled air (ppm)

$C_E$

environmental CO₂ concentrations (ppm)

$c_v$

viral load (copies mL⁻¹)

$c_i$

conversion factor (quanta copies⁻¹)

$E{R}_q$

quanta emission rate (quanta h⁻¹)

$f$

transmission enhancement coefficient

$I$

number of the index case

$I{R}_{cp01}$

individual's infection risk at the short-range scale (0–1 m) (%)

$I{R}_{cp12}$

individual's infection risk at the short-range scale (1–2 m) (%)

$I{R}_{rs}$

individual's infection risk at the room-scale (%)

$k$

deposition rate (h⁻¹)

$m_p$

human body's mass (kg)

$N_1$

number of susceptible individuals at the short-range (0–1 m)

$N_2$

number of susceptible individuals at the short-range (1–2 m)

$N_{rs}$

number of susceptible individuals located at the room-scale

$N_{event}$

total number of individuals

$P_I$

individual's infection probability (%)

$P_{cp01}$

individual's infection probability at the short-range scale (0–1 m) (%)

$P_{cp12}$

individual's infection probability at the short-range scale (1–2 m) (%)

$P_{rs}$

individual's infection probability at the room-scale (%)

$P_{ERq}$

probability of occurrence of each ${ER}_q$

$Q$

outdoor fresh air volume (m³ s⁻¹)

$R_{cp01}$

infection reproduction number at the short-range scale (0–1 m)

$R_{cp12}$

infection reproduction number at the short-range scale (1–2 m)

$R_{rs}$

infection reproduction number at the room-scale

$t$

Exposure duration (h)

$TI{L}_c$

combined total particles inward leakage rate (%)

$TO{L}_c$

combined total particles outward leakage rate (%)

$V$

volume of a shared indoors (m³)

$V_0$

volume of modules (m³)

$V_{net}$

net volume of the compartment (m³)

$V_{jd}$

droplet volume concentration (mL m⁻³)

$x$

distance from the source (m)

Greek symbols

$\gamma$

fraction of infectious aerosols (%)

$\lambda$

virus inactivation rate (h⁻¹)

${\rho }_p$

human body's density (kg m⁻³)

Acronyms

CDC

centers for disease control and prevention

COVID-19

coronavirus disease-2019

CFD

computational fluid dynamics

ET

exposure threshold

ET_i

time interval of exposure threshold

SSEs

super spreading events

SARS-CoV-2

severe acute respiratory syndrome coronavirus 2

TJWR

turbulent jet Wells-Riley

UPT

urban public transport

UVGI

ultraviolet germicidal irradiation

1. Introduction

The COVID-19 pandemic is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which belongs to the family of coronaviruses that can infect humans. This virus is the seventh member of the coronavirus family that can infect humans, as documented in several academic papers [[1], [2], [3]]. To date, multiple variants of SARS-CoV-2 have emerged as prevalent epidemic strains in numerous countries, with several posing significant risks to human health [4]. These include Alpha [5], Beta [6], Gamma [7], Delta [8], and Omicron [9]. According to Ref. [10]; the global death toll from January 1, 2020, to December 31, 2021, exceeded 18 million. From January 2022 onwards, the Omicron variant has become the dominant strain worldwide, with higher transmissibility but lower severity, as reported by Ref. [11]. As of December 2022, almost three years into the COVID-19 pandemic, the number of diagnosed cases reported globally has exceeded 660 million and is still increasing, according to the World Health Organization (WHO) (https://covid19.who.int/table). However, there are likely more additional cases beyond those officially reported to the WHO. China, which is the world's most populous country, ceased reporting the number of infected cases in December 2022. Ongoing research on the transmission mechanism of SARS-CoV-2 has led [12] to propose a more comprehensive definition of the three primary transmission routes as inhalation, spray, and surface contact. Additionally, the airborne transmission route, namely inhalation, deserves more attention considerably than that of surface contact [78], especially for Omicron [13].

Urban public transport (UPT), which includes buses, subways, and high speed trains, is associated with high passenger density, a high crowding index, and variable duration, making it conducive to disease transmission [14,15]. Unlike other modes of transportation such as cycling and private cars, social distancing is difficult to maintain in the limited space of UPT due to high passenger volume. The annual total number of passengers using buses, subways, and high speed trains in China from 2017 to 2021 [76]. Although the total passenger traffic decreased in 2020, it remained at a significant level and continued to increase in 2021, raising concerns about the potential infection risks in UPT. Therefore, it is essential to assess the infection risk and implement measures to ensure the public's inelastic travel needs while preventing the spread of COVID-19.

Numerous studies have investigated the risk of aerosol transmission in UPT systems. Many of these studies, such as those by Refs. [16,17]; have utilized regression or bivariate correlation analyses to demonstrate significant associations between UPT use and infection incidence. Based on a regression analysis of data from the location-based services database [18], identified a robust and statistically significant correlation between train travel and the incidence of 2019-nCoV cases. Furthermore [16], reported significant positive linear correlations between trip frequency (i.e., flights, buses, and trains), and case incidence (i.e., daily or cumulative) in China. Based on fixed effects regression modeling [19], found that reductions in mobility had a prominent effect on reproduction numbers [20]. reported that the attack rate decreased with increasing social distance, but increased with increasing co-travel time on high speed trains, based on their study. However, the studies mentioned above have not provided a comprehensive quantitative analysis of infection risk at transmission scales in UPT. The transmission scale can be vital in assessing and mitigating risks [75]. Indoor transmission scenarios in Fig. 1 are divided into short-range and room-scale [21]. The room-scale transmission is thought to represent long-distance transmission [22], with susceptible individuals in shared indoor spaces being at a distance of more than 2 m from an infected person (denoted as an index case). The short-range transmission is defined as a distance of less than 2 m or 6 feet between two individuals in many papers [[23], [24], [25], [77]].

Fig. 1.

Illustration of the relationship between short-range and room-scale exposure in confined indoor environments [21].

Many transmissions and even super spreading events (SSEs) have been induced by asymptomatic individuals without sneezing or coughing, which has contributed to the rapid spread of COVID-19 in crowded indoor environments with poor ventilation [[26], [27], [28]]. Furthermore, individuals breathe much more frequently than they cough, and thus, quiescent breathing or speaking might generate more airborne particles containing infectious viruses over time [75] [29]. demonstrated that poor ventilation, i.e., insufficient air changes per hour (ACH), increased the risk of respiratory infections at the short ranges. However, the impact of various non-pharmacological interventions, such as maintaining social distance, increasing ventilation, and wearing masks, as well as the effects of COVID-19 variants (e.g., Delta and Omicron), respiratory activities (e.g., quiescent breathing or speaking), and other factors on transmission risks, has not been adequately quantified.

This study aims to quantify the transmission risks in crowded UPT settings, such as buses, subways, and high speed trains, and to identify effective non-vaccine control strategies for reducing potential transmission in the post-COVID era. Therefore, careful evaluation of the multi-scale risks in closed environments of the UPT with insufficient ventilation is necessary [4]. The paper is structured as follows. Section 2 presents the overall infection risk assessment method and the background of field measurements and modeling in the three typical UPT, including buses, subways, and high speed trains. Section 3 presents the analysis of assessment results of the infection risk and reproduction number and a comparison of mitigations on the reduction level of risks. Finally, the discussion is presented in Section 4, with the conclusions drawn in Section 5.

2. Methods

In this study, we evaluated the short-range and room-scale risks in buses, subways, and high speed trains based on the COVID-19 risk assessment model proposed by Ref. [25]. Field measurements were conducted to provide data on typical passenger behaviors and ACH.

2.1. Estimation of the ventilation rate

Based on field measurements of CO₂ concentrations in compartments and the CO₂ tracer gas-decay method, exhaled concentrations through breathing, the number of total passengers, outdoor fresh air volume $Q$ (m³ s⁻¹), and ACH (h⁻¹) can be calculated using Eqs. (1), (2), (3) proposed by Refs. [30,31].

$$V_{net}=V-V_0-N_{event}\times \frac{m_p}{{\rho }_p}$$ (1)

$$V_{net}\times \frac{C_2-C_1}{△t}=N_{event}\times BR\times C_a+\left(C_E-\bar{C}\right)\times Q$$ (2)

$$ACH=\frac{3600\times Q}{V_{net}}$$ (3)

where $V_{net}$ (m³) is the air volume of the enclosure; $V$ (m³) is the total volume of the enclosure; $V_0$ (m³) is the volume of modules occupied by the seats, transitional steps, air ducts on both sides of the interior compartment, and among others, which are calculated and subtracted; $m_p$ (kg) is the human's body mass; ${\rho }_p$ (kg m⁻³) is the human's body density, using a mean body mass of 70 kg and a density of 1.01 × 10³ kg m⁻³ [32]; $BR$ (m³ s⁻¹) is the breathing rate of individuals; which is determined by activity levels and is approximately 1.36 × 10⁻⁴ m³ s⁻¹ and 1.50 × 10⁻⁴ m³ s⁻¹ for resting and standing, respectively [33]. and $C_2$ (ppm) are the CO₂ concentrations at time t ₁ and time t ₂, respectively; $△t$ (s) is the calculation period, i.e., $△t$ = t ₂-t ₁; $C_a$ is the fraction of CO₂ contained in the exhaled air, which is commonly assumed to be 4% based on previous studies [34]; $C_E$ (ppm) is environmental CO₂ concentration with a typical value of 400 ppm [35,36]; $\bar{C}$ (ppm) is the average CO₂ concentration during the period $△t$; and $N_{event}$ represents the total number of individuals in a closed environment shared with an infected person. To measure the real-time CO₂ concentrations, three portable multifunctional composite gas analyzers (JK90-M9, Gishunan Technology Shenzhen, China) equipped with CO₂ sensors with a range of 0–10,000 ppm and a resolution of 1 ppm were used. The passenger behaviors were recorded with micro-network cameras (V8-8, Suodun, Dongguan, China). ACH was calculated when the number of passengers was maintained relatively stable. In summary, the values of $V$, $V_0$, $C_1$, $C_2$, $△t$, and $N_{event}$ were derived from field measurements and video recordings, while the values of $m_p$, ${\rho }_p$ $BR$, $C_E$, and $C_a$ were obtained from the literature [[32], [33], [34], [35], [36]]. The measurement routes used in this study included Hangzhou Bus Line 193 (model type: BYD K9A), Hangzhou Subway Line 2 (model type: Type B), and a high speed train (model types: CR400 or CRH 300) from Hangzhou to Shanghai, as marked in Fig. 2 . Further information on the measurement routes is provided in Table 1 .

Fig. 2.

Traffic routes of (a) buses Line 193; (b) subways Line 2; (c) high speed trains CR400 and CRH300; (d) snapshots in crowded circumstances.

Table 1.

Detailed geometry and route information on buses, subways, and high speed trains.

Types	Bus (BYD K9A)	Subway (Type B)	Trains (CR400, CRH300)
Length × Width × Height (m)	12.0 × 2.5 × 2.7	20.0 × 2.88 × 2.1	25.8 × 3.66 × 2.8
$V_0$ (m3)	12.4	7.3	15.3
Distance of the whole trip (km)	23	43.3	160
Duration of the whole trip	1.5 h	1.5 h	4 h
$N_{event}$ (full load condition)	80	240	90
Seats	40	41	90
$N_1/N_2$a	5/10	8/15	2/7
The time between two subsequent stops (min)	3–5	1–4	18–60
Measured datesb	2021-03-08, 03–10, 05–10, 05–12, and 05-15	2021-03-18, 06-03, 06-05, and 07-29	2021-02-21, 02–23, 03–05, 03–11, 03–16, 03–19, 03–23, 04-02, 04–16, and 05-28
Peak periodsd	7:00–9:30, 11:30–13:00, and 16:30–19:00	6:00–10:30, 16:30–19:00	NAc
Off-peak periodsd	9:30–11:30, 13:00–16:30, and 19:00–22:00	10:30–16:30, and 19:00–23:00	NA

^a$N_1$ and $N_2$ are the number of individuals located at short-range 1 (0–1 m distance from the index case) and short-range 2 (1–2 m distance from the index case), respectively, as shown in Fig. 3.

^bIncluding two typical measured dates, namely weekdays and weekends during spring and summer.

^c‘NA’ represents no typical peak or off-peak periods for high speed trains.

^dThe peak and off-peak periods are determined based on the fundamental characteristics of intra-city traffic on weekdays, and combined with video recordings taken during the measurements.

Based on the actual geometric size, layout, and passenger behaviors recorded on video, top views of buses, subways, and high speed trains in crowded conditions (full load condition) are illustrated in Fig. 3 followed by Ref. [37]. The locations of CO₂ sensors and cameras are marked in Fig. 3. The locations of the index case and susceptible individuals within short-range 1 and 2 were indicated by red and light red shading. Four types of activities, including quiescent breathing + resting, quiescent breathing + standing, speaking + resting, and speaking + standing, were considered. Different characteristic zones have been classified in UPT (Fig. 3), including seating zone A (marked by a blue frame) and standing zone B (marked by a yellow frame). In subways, standing zone B is further divided into standing zone B1-door and standing zone B-window (Fig. 3b). To determine the highest contact rates between infected and susceptible passengers, the index case is located in the standing zones, as these areas typically have the highest contact rates. In the case of “standing zone B″ in high speed trains, it was found that salespersons and a few standing ticket passengers stayed for longer periods. During the actual measurements, the subway compartments were crowded with passengers. To improve the readability of Fig. 3b and due to the high consistency of activity characteristics within the same zone, passengers in the remaining zones of Fig. 3b are not drawn simultaneously.

Fig. 3.

The top views of the behavioral activity characteristic zone of passengers, testing locations, camera locations, and location of the index case in the compartment. (a) buses line 193; (b) subways line 2; (c) high speed trains CR400 and CRH300.

2.2. Evaluation of the individual's infection risk

In the TJWR model, the quanta emission rate ($E{R}_q$, quanta h⁻¹) is an essential parameter for infection risk assessments [25]. To obtain this parameter, a forward calculation method (Eq. (4)) is applied based on the viral load, type of respiratory activity, respiratory parameters, and activity level [38]. The forward calculation method allows for easy accessibility of each relevant parameter, in contrast to the backward calculation method (retrospective assessments), which depends on critical factors such as actual infection rate, actual ventilation, exposure duration, and respiratory activity. The backward calculation method was applied to estimate the $E{R}_q$ of an infector based on a real infectious outbreak only at the end of an epidemic [39]. However, one of these critical details is often partially missing, and building data are difficult to obtain, even though significant outbreaks have been documented [40]. Therefore, the forward calculation method is employed in this study, which is also useful for evaluating the impact of different respiratory activities on infection risk [41].

$$E{R}_q=f\times c_v\times c_i\times B{R_i}_c\times V_{jd}$$ (4)

where $c_v$ (copies mL⁻¹) is the viral load of an index case. The average and standard deviation of ${\log }_{10}{c}_v$ is equal to 7 and 0.71, respectively [41]; $c_i$ (quanta copies⁻¹) is a conversion factor expressed by $c_i=1/\left(c_{RNA}\times c_{PFU}\right)$. The average (±standard deviation) of $c_{RNA}$ (copies PFU⁻¹) and $c_{PFU}$ (PFU quanta⁻¹) are equal to 210(±21) and 130(±13) respectively [41]; $B{R}_{ic}$ (m³ h⁻¹) is the exhalation rate of an index case, i.e. the same value as $BR$ taken in Eq. (3); $V_{jd}$ (mL m⁻³) is the droplet volume concentration exhaled by an index case, which also depends on respiratory activities (e.g., breathing and speaking). The average (±standard deviation) of $V_{jd}$ for breathing and speaking is equal to 2 × 10⁻³ (±5 × 10⁻⁴) and 9 × 10⁻³ (±2 × 10⁻³), respectively [41,42]; $f$ represents the transmission enhancement coefficient, which is defined as the $E{R}_q$ ratio of the Pre-Delta strain to different variant strains (e.g., Delta or Omicron). Combining with the basic reproduction number ($R_o$), the value of $E{R}_q$ in $f$ is determined by the fitting curve from the study conducted by Ref. [43]. $f$ is equal to 1, 10.8, and 30.1 for Normal, Delta, and Omicron, respectively [25]. The background quanta concentration ($C_r$) in confined indoor environments ($V_{jd}$, quanta m⁻³) can be calculated with Eq. (5). We consider that $C_r$ is perfectly mixed in Eq. (5), in line with the assumption made by Refs. [23,44]; and [41].

$$V_{net}\times \frac{d{C}_r}{dt}=E{R}_q\times I-IVRR\times V_{net}\times C_r$$ (5)

where $C_{ro}$ (quanta m⁻³) denotes the initial quanta concentration in shared indoor environments (generally assumed to be zero); $I$ is the number of the index case (generally assumed to be constant); $t$ (h) is the exposure duration of the index case; and $IVRR$ (h⁻¹) is the removal rate of the infectious virus, which can be attributed to the following three factors [45]. First, ACH, based on the volume of virus-free air, which depends on the volume of fresh outdoor air, volume filtration of the returned air (HEPA), and volume of air goes through ultraviolet germicidal irradiation (UVGI) [9]. Second, the deposition rate of infectious particles on surfaces due to gravity, $k$ (h⁻¹), with a typical value of 0.24 h⁻¹ [46]. Third, the virus inactivation rate, $\lambda$ (h⁻¹), has a typical value of 0.63 h⁻¹ [47]. Combining $C_r$ calculated by Eq. (5) with the steady-state mass conservation law near the index case and susceptible individuals ($x$ ≤ 2 m) and the turbulent jet theory, the quanta concentration $C$ at the inhalation position is written as Eq. (6). According to the dilution coefficient of the jet and the typical human mouth diameter of $D=20$ mm, the average dilution ratio of aerosol concentration $\bar{S}$ can be written as $0.32x/D$ [23,48]. Thus the TJWR model can be written as Eq. (7) to calculate the individual's infection probability ($P_I$). The susceptible individual's infection probability at the room-scale ($P_{rs}$) can be obtained by Eq. (8). By combining with $P_{rs}$ (Eq. (8)) and the probability of occurrence of each $E{R}_q$ ($P_{E{R}_q}$), the infection risk at the room-scale ($I{R}_{rs}$) can be obtained with Eq. (9).

$$C=C_r+\frac{D}{0.32x}\times \left(C_o-C_r\right)$$ (6)

$$P_I=1-\exp \left\{-TI{L}_c\times TO{L}_c\times B{R}_{si}\times {\int }_0^t\left[C_r+\frac{D}{0.32x}\left(C_o-C_r\right)\right]dt\right\}$$ (7)

$$P_{rs}=1-\exp \left(-TI{L}_c\times TO{L}_c\times B{R}_{si}\times {\int }_0^t{C}_{r}dt\right)(\mathrm{R}\mathrm{o}\mathrm{o}\mathrm{m}-\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e})$$ (8)

$$I{R}_{rs}={\int }_{E{R}_q}\left[P_{E{R}_q}\times P_{rs}\right]dE{R}_q(\mathrm{R}\mathrm{o}\mathrm{o}\mathrm{m}-\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e})$$ (9)

where $C_o$ (quanta m⁻³) is the quanta concentration released by the index case, i.e., $C_o=E{R}_q/\left(\gamma \times B{R}_{ic}\right)$; $x$ (m) is the distance from the source along the flow direction; $B{R}_{si}$ (m³ h⁻¹) is the inhalation rate of susceptible individuals; $TI{L}_c$ (%) is the combined total particles inward leakage rate of the mask worn by susceptible individuals; and $TO{L}_c$ (%) is the combined total particles outward leakage rate of the mask worn by an index case [49]. Since the viral load is assumed to share the same concentration for each virus-laden aerosol or droplet [50,51], $TI{L}_c$ and $TO{L}_c$ can be defined as the ratio of total volume inside and outside masks, instead of the number concentration. In contrast to large particles, more small particles exhaled by the index case are lower in volume (lower quanta concentration) [44,52,53]. In addition, small particles have a higher probability of penetrating masks because masks are generally less effective in filtering small particles compared to large particles [49]. When defining the filtering efficiency of masks as a ratio of the number of particles inside and outside masks, a lower value of filtering efficiency is obtained. Therefore, based on a more reasonable volume concentration inside and outside masks, $TI{L}_c$ and $TO{L}_c$ can be written as Eq. (10) and Eq. (11) respectively.

$$TO{L}_c=\frac{{\sum }_{i=\mathrm{1,2,3}}^{j=s,b}TO{L}_i\times F_{i,j}\times d_i^3}{{\sum }_{i=\mathrm{1,2,3}}^{j=s,b}{F}_{i,j}\times d_i^3}$$ (9a)

$$TI{L}_c=\frac{{\sum }_{i=\mathrm{1,2,3}}^{j=s,b}TI{L}_i\times TO{L}_i\times F_{i,j}\times d_i^3}{{\sum }_{i=\mathrm{1,2,3}}^{j=s,b}TO{L}_i\times F_{i,j}\times d_i^3}$$ (10)

where $F_{i,j}$ represents the proportion of different particle sizes ($i$ = 0.3–1.0 μm; 1.0–3.0 μm; 3.0–10 μm) when breathing ($j=b$) and speaking ($j=s$); $d_i$ is the typical diameter (0.7 μm, 2.0 μm, and 6.0 μm for 0.3–1.0 μm, 1.0–3.0 μm, and 3.0–10 μm, respectively); and $TO{L}_i$ represents the outward leakage rate of masks for particles with a particle size of $i$. The values of $F_{i,j}$ and $TO{L}_i$ ($TI{L}_i$) are shown in Table 2 . The values of $TI{L}_c$ and $TO{L}_c$ are presented in Table 3 .

Table 2.

The particle size distribution ($F_{i,j}$) of speaking and breathing, and $TO{L}_i$ ($TI{L}_i$) of surgical masks, FFP2 masks, and FFP2-WD. FFP2-WD represents that FFP2 masks are well-adjusted.

Respiratory activity and type of masks		$F_{i,j}$
		0.3–1.0 μm	1.0–3.0 μm	3.0–10 μm
Initial particle size distribution (Morawska et al., 2009; Riediker & Tsai. 2020; Harmon & Lau. 2021)	Speaking	57%	37%	6%
	Breathing	72%	26%	2%
$TO{L}_i$ ($TI{L}_i$) (Bagheri et al., 2021)	Surgical masks	67%	35%	9%
	FFP2 masks	53%	25%	7%
	FFP2-WD	24%	8%	1%

Table 3.

$TO{L}_c$ and $TI{L}_c$ for different respiratory activities. It is assumed that susceptible individuals and the index case wear the same type of mask in each scenario.

Particle leakage rate		Surgical masks	FFP2 masks	FFP2-WD
$TO{L}_c$	Speaking	14.5%	10.9%	2.6%
	Breathing	19.3%	14.3%	4.0%
$TI{L}_c$	Speaking	23.8%	17.3%	7.6%
	Breathing	31.2%	23.1%	10.4%

During quiescent breathing and speaking, the virus-laden aerosol concentration is higher near the source in the jet zone at the short-range, which poses a higher risk during face-to-face interaction with an index case. Airborne transmission risk at the short-range is evaluated using the jet equation, which considers the aerosol concentration as a function of distance x (x ≤ 2 m) in the jet zone [23,54]. A threshold distance of 2 m seems to be effective under the assumption of an ideal steady jet based on the study of [55]. The locations at x = 0.5 m and x = 1.5 m are used as the representative values for short-range 1 (0–1 m) and short-range 2 (1–2 m), respectively. Similarly to the calculation of $P_{rs}$, the susceptible individual's infection probability at the short-range ($P_{cp01}$ and $P_{cp12}$) can be obtained by Eqs. (12), (13). The infection probability $P_{cp01}$ (short-range 1) and $P_{cp12}$ (short-range 2) (%) in the two sub-zones mentioned above can be written as Eqs. (12), (13), respectively.

$$P_{cp01}=1-\exp \left\{-TI{L}_c\times B{R}_{si}\times E{R}_q\times \left[\frac{0.125t}{\gamma \times B{R}_{si}}+\frac{0.875}{V_{net}\times IVRR}\times \left(\frac{IVRR\times t+\exp \left(-IVRR\times t\right)-1}{IVRR}\right)\right]\right\}(\mathrm{S}\mathrm{h}\mathrm{o}\mathrm{r}\mathrm{t}-\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}1)$$ (12)

$$P_{cp12}=1-\exp \left\{-TI{L}_c\times B{R}_{si}\times E{R}_q\times \left[\frac{0.042t}{\gamma \times B{R}_{si}}+\frac{9.985}{V_{net}\times IVRR}\times \left(\frac{IVRR\times t+\exp \left(-IVRR\times t\right)-1}{IVRR}\right)\right]\right\}(\mathrm{S}\mathrm{h}\mathrm{o}\mathrm{r}\mathrm{t}-\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}2)$$ (13)

where $\gamma$ is the fraction of infectious aerosols in suspended aerosols in the expired jet that remain suspended in the room-scale zone [23]. Assuming perfectly mixed indoor air and the mass conservation law, $C_r$ can be obtained. Similarly, steady-state mass conservation law near the index case and susceptible individuals (x ≤ 2 m), and $\gamma$ is introduced to calculate $C_o$ [23]. Thus, the quanta concentration at the inhalation position of the susceptible individuals within the short-range can be obtained [25]. Here, $\gamma$ is assumed to be 50% based on the research by Ref. [23]. It is worth noting that when an index case wears a mask, the exhaled jet containing high virus concentrations can be blocked by the mask, and its dispersal can be disrupted. The study by Ref. [56] found that the total aerosol concentration level measured in front of the mask was similar to the room's background level. Therefore, in this paper, the calculation of risks at the short-range 1 and 2 ($P_{cp01}$ and $P_{cp12}$) refers to Eq. (8), i.e., the same infection probability as at the room-scale ($P_{rs}$). Similarly, for the short-range scale, risks of the two sub-zones short-range 1 and 2 are expressed as $I{R}_{cp01}$ (%) and $I{R}_{cp12}$ (%), respectively, and calculated using Eqs. (14), (15), respectively.

$$I{R}_{cp01}={\int }_{E{R}_q}\left[P_{E{R}_q}\times P_{cp01}\right]dE{R}_q(\mathrm{S}\mathrm{h}\mathrm{o}\mathrm{r}\mathrm{t}-\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}1)$$ (14)

$$I{R}_{cp12}={\int }_{E{R}_q}\left[P_{E{R}_q}\times P_{cp12}\right]dE{R}_q(\mathrm{S}\mathrm{h}\mathrm{o}\mathrm{r}\mathrm{t}-\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}2)$$ (15)

The infection reproduction number for the room-scale and short-range are denoted as $R_{rs}$ and $R_{cp}$, respectively, which can be obtained with Eqs. (16), (17), (18). Moreover, the total infection reproduction number ($R$) can be calculated using Eq. (19).

$$R_{rs}=I{R}_{rs}\times N_{rs}(\mathrm{R}\mathrm{o}\mathrm{o}\mathrm{m}-\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e})$$ (16)

$$N_{rs}=\left(N_{event}-N_1-N_2-1\right)$$ (17)

$$R_{cp}=R_{cp01}+R_{cp12}=N_1\times IR{}_{cp01}+N_2\times I{R}_{cp12}(\mathrm{S}\mathrm{h}\mathrm{o}\mathrm{r}\mathrm{t}-\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e})$$ (18)

$$R=R_{cp}+R_{rs}$$ (19)

where $R_{cp01}$ and $R_{cp12}$ represent the infection reproduction number at the short-range 1 and 2, respectively; and $N_{rs}$ represents the number of susceptible individuals located at the room-scale.

3. Results

3.1. Statistics of CO₂ concentrations and calculation of ACH in UPT

Based on the field measurements, boxplots of CO₂ concentrations in buses, subways, and high speed trains are plotted in Fig. 4 . According to the chronological order of measured dates in Table 1, different dates are named as follows. For example, measurements in buses on different dates are denoted as Case1-B to Case5-B respectively. Similarly, measurements in subways and high speed trains are denoted as Case1-S to Case4-S and Case1-H to Case10-H respectively. The terms “Cases-B″, “Cases-S″, and “Cases-H″ represent the aggregated measurements.

Fig. 4.

The boxplots of CO₂ concentrations on different measured dates. (a) buses; (b) subways; (c) high speed trains.

As shown in Fig. 4a, for different measured dates, the average CO₂ concentration during the peak periods and off-peak periods ranged from 813 ppm to 2967 ppm, from 407 ppm to 1569 ppm, respectively [57]. conducted field sampling in buses with an arithmetic average CO₂ concentration of 959 ppm, which agreed with our results. Similarly, in subways, the average CO₂ concentration during the peak and off-peak periods ranged from 757 ppm to 1245 ppm, from 627 ppm to 890 ppm, respectively. For Cases-B and Cases-S, the average CO₂ concentration during the peak periods was 2.2-folds and 1.3-folds higher than in off-peak periods, respectively. The CO₂ concentrations (ranging from 1160 ppm to 1550 ppm) in high speed trains are relatively stable, which is related to the relatively strict control of the environmental parameters. The average CO₂ concentration in buses was the highest, which was nearly 1.8-folds greater than in subways and 1.4-folds greater than in high speed trains. For buses, when setting the air conditioning system to the recirculation mode with closed windows and at a low driving speed, the fresh air would be greatly reduced, resulting in elevated CO₂ concentrations in buses [57,58]. High CO₂ concentration is an indicator of inadequate ventilation, which can lead to high infectious aerosol concentrations and increase the transmission risks of COVID-19 [14]. Moreover, prolonged exposure of passengers and drivers to high CO₂ concentration can cause sleepiness, fatigue, and even decision-making performance [59].

Based on Eqs. (1), (2), (3), ACH is calculated and shown in Fig. 5 . As all windows in buses are openable, passengers have the opportunity to increase ventilation by opening windows for fresh air. Videos recorded during field measurements indicated a higher frequency of passengers opening windows in May during the measurements of Case3-B, Case4-B, and Case5-B. The opening of windows tends to significantly increase the value of ACH. Therefore, measurements in buses were divided into two groups, i.e., Group 1-B (Case1-B and Case2-B), and Group 2-B (Case3-B, Case4-B, and Case5-B). The average ACH in Group 2-B was 2.7-folds higher than in Group 1-B due to the opening of windows.

Fig. 5.

Calculated ACH for buses, subways, and high speed trains.

As displayed in Fig. 5, the ACH of buses, subways, and high speed trains ranged from 2 h⁻¹ to 20 h⁻¹ (9 h⁻¹ on average), 8 h⁻¹ to 22 h⁻¹ (16 h⁻¹ on average), and 4 h⁻¹ to 11 h⁻¹ (8 h⁻¹ on average), respectively. Therefore, the typical values of ACH can be set as 5 h⁻¹, 10 h⁻¹, and 15 h⁻¹ for buses, 10 h⁻¹, 15 h⁻¹, and 20 h⁻¹ for subways, and 5 h⁻¹ and 10 h⁻¹ for high speed trains. These values will be used as subsequent inputs in the TJWR model to assess the risks of COVID-19 transmission. According to $N_{event}$ in Table 1 and typical values of ACH, and it is assumed that the total passengers are 100%, 75%, 50%, and 25% of $N_{event}$, respectively, ventilation rate per person (L s⁻¹ p⁻¹) could be obtained. The corresponding results are shown in Fig. 6 . According to Ref. [75], the typical, poor, and high ventilation rate per person is defined as 5–10 L s⁻¹ p⁻¹, less than 3 L s⁻¹ p⁻¹, and more than 25 L s⁻¹ p⁻¹, respectively for highly occupied space. It is assumed in this study that each circumstance (rectangular cell in Fig. 6) occurs with an equiprobable event in terms of total passengers and ACH. Fig. 6 indicates that the proportion of below-typical (<5 L s⁻¹ p⁻¹)/poor (<3 L s⁻¹ p⁻¹) ventilation scenarios is 75%/33% for buses, 75%/50% for subways, and 13%/0% for high speed trains, respectively. Moreover, when the total passenger is 25% of N _event, the ventilation rate can satisfy the typical value.

Fig. 6.

The calculated ventilation rate per person in buses, subways, and high speed trains with typical values of ACH and total passengers.

However, as the total passenger increased, the ventilation rate per person decreased significantly and could even reach 1.1 L s⁻¹ p⁻¹. When it increased to 50% of N _event for the subways and 75% of N _event for buses, the ventilation rate per person was less than 5 L s⁻¹ p⁻¹ regardless of ACH. Therefore, for buses and subways, when the total passenger exceeded 50% of N _event, additional fresh air must be supplied. For high speed trains, the ventilation rate per person was less than 5 L s⁻¹ p⁻¹ only when ACH was equal to 5 h⁻¹ and the total passenger was 100% of N _event. The above findings highlight the importance of conducting infection risk assessments for high-occupancy UPT systems in the post-epidemic era.

3.2. Infection risk assessments at the short-range and room-scale

Based on Eq. (8) and Eqs. (13), (14), assuming that the index case is quiescent breathing or speaking with minimum typical ventilation (ACH = 5 h⁻¹ for buses; ACH = 10 h⁻¹ for subways; ACH = 5 h⁻¹ for high speed trains), $I{R}_{cp01}$, $I{R}_{cp12}$, and $I{R}_{rs}$ are calculated. According to the principle that R is less than 1, two parameters of time-scale based exposure thresholds are proposed, i.e., the infectious exposure threshold (h) (ET: duration when $R_{rs},R_{cp01},R_{cp12}=0.5$) and the time interval of exposure threshold (h) (ET_i: the duration interval when $R_{rs},R_{cp01},R_{cp12}=0.5-1.5$). Based on the rounding principle, ET represents the possible minimum duration when $R_{rs},R_{cp01},R_{cp12}=1$. ET_i represents the time interval of the exposure threshold when $R_{cp01}$, $R_{cp12}$, and $R_{rs}$ are approximately equal to 1. That is, there is a possibility that the reproduction number is equal to 1 at any moment within this interval ET_i. ET and ET_i can guide for the public to avoid overstaying. Results of infection risk assessment at the multi-scale are illustrated in Fig. 7 . The respiratory status of the index case is presented using a cube (square) and a sphere (circle) to represent breathing and speaking, respectively.

Fig. 7.

$I{R}_{cp01}$, $I{R}_{cp12}$, and $I{R}_{rs}$ considering different variants (Normal, Delta, and Omicron) versus exposure duration under the minimum typical ventilation (ACH = 5 h⁻¹ for buses; ACH = 10 h⁻¹ for subways; ACH = 5 h⁻¹ for high speed trains). (a) buses; (b) subways; (c) high speed trains.

The infection risk threshold is defined as the minimum risk value when $R_{rs},R_{cp01},R_{cp12}\approx 1$, which depends on the number of passengers at the short-range and room-scale. The infection risk thresholds at different scales are marked in Fig. 7 with grey horizontal planes, with circumstances above grey planes filled with red solid symbols (early warning), and others filled with green hollow symbols. Based on $N_1/N_2/N_{event}$ in Table 1, the infection risk threshold at the short-range 1 was 7.1%, 6.3%, and 25.0%, and those for short-range 2 were 4.2%, 3.4%, and 7.1%, respectively. The infection risk threshold at the room-scale was 0.78%, 0.23%, and 0.62%, respectively.

For Delta or Omicron, although the index case keeps quiescent breathing, $R_{cp}\ge 1$ still occurs less than 0.1 h with a shorter ET. At the short-range, the infection risk threshold in subways was approximately 11.3% (short-range 1) and 19.0% (short-range 2) less than in buses. Similarly, the infection risk threshold in buses was 71.6% (short-range 1) and 40.8% (short-range 2) less than in high speed trains. $I{R}_{rs}$ was still also high for Delta and Omicron, and the respiratory activity of speaking caused a shorter infection risk threshold compared with breathing. At the room-scale, the threshold in subways was 70.5% less than in buses, and the threshold in buses was 25.8% higher than in high speed trains. It should be noted that subways have the highest risks among the three types of UPT, as shown by the results obtained from the short-range and room-scale risk assessments. Based on ordinary least squares analysis [60], also noted a significant influence of public transport (i.e. subways) on the prevalence of COVID-19. Furthermore, the ET at the short-range was lower than at the room-scale, which demonstrates that $I{R}_{cp01}$ and $I{R}_{cp12}$ are extremely high and it is crucial to maintain social distance between passengers.

3.3. Influence of ACH on $I{R}_{cp01}$, $I{R}_{cp12}$, and $I{R}_{rs}$

Reduction level of $I{R}_{cp01}$, $I{R}_{cp12}$, and $I{R}_{rs}$ were evaluated if the index case had different respiratory activities in typical values of ACH (i.e., 5 h⁻¹ and 15 h⁻¹ for buses; 10 h⁻¹ and 20 h⁻¹ for subways; 5 h⁻¹ and 10 h⁻¹ for high speed trains). The reduction level of risks was counted and averaged for different exposure durations (duration interval: 0.2 h for buses, 0.2 h for subways, and 0.5 h for high speed trains, respectively). Results are shown in Fig. 8 . When the increase of ACH, there was only a slight reduction in $I{R}_{cp01}$ and $I{R}_{cp12}$, but can result in a significant reduction level for room scales. In addition to this, it is found that the reduction level of risks tends to reach a stable value with increasing exposure duration.

Fig. 8.

Reduction level of $I{R}_{cp01}$, $I{R}_{cp12}$, and $I{R}_{rs}$ versus exposure duration When ACH increases from the minimum to the maximum typical value. (a) buses, (b) subways, (c) high speed trains.

At the short-range 1, $I{R}_{cp01}$ decreased by an average of 4%, 2%, and 3% in buses, subways, and high speed trains, respectively. At the short-range 2, $I{R}_{cp12}$ decreased by an average of 7%, 6%, and 9% in buses, subways, and high speed trains, respectively. Results indicate that increasing ACH does not reduce $I{R}_{cp01}$ and $I{R}_{cp12}$ significantly but more obviously for $I{R}_{cp12}$. At the room-scale, $I{R}_{rs}$ decreased by an average of 55%, 42%, and 41% in buses, subways, and high speed trains, respectively, which show that is more effective to reduce $I{R}_{rs}$ compared to reducing $I{R}_{cp01}$ and $I{R}_{cp12}$. For quiescent breathing, increasing ACH leads to a generally higher reduction level of risks than speaking, with an increase of 34.1% at the short-range 1, 19.9% at the short-range 2, and 7.6% at the room-scale, respectively. To improve the reduction effect of increasing ACH, it is encouraged to speak less frequently when travelling with urban public transport, especially for short-range scale.

For the passengers, they can adjust their location to ensure as much safety as possible, which is defined as the maximum number of passengers allowed to be exposed at the short-range, i.e., $N_1$ and $N_2$). Two exposure duration scenarios are discussed, namely the entire trip and half the trip. the results of which are shown in Table 4 .

Table 4.

Spatial-scale based upper limit warnings of $N_1$ and $N_2$ at the short-range.

Type	ACH, h−1	Speaking				Breathing
		$N_1$-wb	$N_2$-w	$N_1$-hc	$N_2$-h	$N_1$-w	$N_2$-w	$N_1$-h	$N_2$-h
Buses	5	1/0/0a	1/0/0	2/0/0	2/0/0	2/0/0	5/1/0	3/1/0	8/1/1
	10	1/0/0	1/0/0	2/0/0	2/0/0	2/0/0	5/1/0	3/1/0	8/1/1
	15	1/0/0	2/0/0	2/0/0	3/1/0	3/1/0	5/1/1	4/1/1	9/2/1
Subways	10	1/0/0	1/0/0	2/0/0	2/0/0	2/0/0	5/1/0	3/1/0	8/1/1
	15	1/0/0	1/0/0	2/0/0	2/0/0	2/0/0	5/1/0	3/1/0	8/1/1
	20	1/0/0	2/0/0	2/0/0	3/1/0	3/1/0	5/1/1	4/1/1	9/2/1
Trains	5	1/0/0	1/0/0	2/0/0	2/0/0	2/0/0	5/1/0	3/1/0	7/1/1
	10	1/0/0	2/0/0	2/0/0	2/1/0	3/1/0	5/1/1	4/1/1	7/2/1

^a1/0/0 represents the limit warnings of $N_1$ for Normal, Delta, and Omicron is 1, 0, and 0, respectively.

^b‘w’ represents the exposure duration of the whole trip and half the trip for buses, subways, and high speed trains.

^c‘h’ represents the exposure duration of the whole trip and half the trip for buses, subways, and high speed trains.

Even though the ventilation is high (ACH = 15 h⁻¹ for buses, 20 h⁻¹ for subways, and 10 h⁻¹ for trains), the principle of maintaining a distance of over 2 m still needs to be considered, especially if the index case keeps speaking for Omicron. Increasing ACH has only a slight effect on the short-range, as shown in Fig. 8. As an “imperfect barrier to spread”, however, screening ill individuals tends to miss 50–75% of the index cases [61]. This is mainly because, during the incubation period, some individuals may be asymptomatic, which makes their recognition challenging [26]. Therefore, it is crucial to consider every passenger as a potential source of infection. Based on the real-time compartment environments, the public can refer to the recommended value in Table 4 as guidance.

Similarly, for transit operators, a spatial-scale based upper limit warning is proposed to reasonably control occupancy rates of UPT ($N_{event}$). the spatial-scale based upper limit warnings of $N_{event}$ in buses, subways, and high speed trains are depicted in Table 5 . The modification of the limit warning was initially performed by considering the maximum occupancy in the compartment, as presented in Table 1. We define $N_{event-co}$ as the rough total number in the compartment (estimated) for the limit warnings of $N_1$ and $N_2$. Since the $N_{event-co}$ is a rough estimate, $N_{event-co}$ is determined based on the fact that passengers prefer to choose the seating zone, i.e., they sit down and do not stand first if a seat is available. $N_{event-s}$ is also defined as the limit warning obtained from the TJWR model. In this paper, the focus is not on the exact value of $N_{event-co}$ but on only comparing the relationship between the values of $N_{event-co}$ and $N_{event-s}$. In a particular case, for scenarios of $N_1=4$ and $N_2=9$ for buses, $N_1=4$ and $N_2=9$ for subways, and $N_1=4$ and $N_2=7$ for trains, it is difficult to obtain the exact $N_{event-co}$.

Table 5.

Spatial-scale based upper limit warnings of $N_{event}$.

Type	ACH, h−1	Speaking		Breathing
		$N_{event}$-w	$N_{event}$-h	$N_{event}$-w	$N_{event}$-h
Buses	5	NRa/6/2	NR/NR/4	NR/19/6	NR/NR/NR
	10	NR/NR/4	NR/NR/7	NR/NR/NR	NR/NR/NR
	15	NR/NR/6	NR/NR/NR	NR/NR/NR	NR/NR/NR
Subways	10	NR/NR/7	NR/NR/12	NR/NR/NR	NR/NR/NR
	15	NR/NR/9	NR/NR/NR	NR/NR/NR	NR/NR/NR
	20	NR/NR/11	NR/NR/NR	NR/NR/NR	NR/NR/NR
Trains	5	NR/7/3	NR/13/6	NR/NR/11	NR/NR/22
	10	NR/12/5	NR/NR/9	NR/NR/NR	NR/NR/NR

^a‘NR’ represents not being required once spatial-scale based limit warnings of $N_1$ and $N_2$ are satisfied.

However, it is evident that the relationship between the values of $N_{event-co}$ and $N_{event-s}$ can be determined. When the value of $N_{event-co}$ is lower than $N_{event-s}$, R can be reduced to less than 0 by maintaining the requirement of $N_1$ and $N_2$ (Table 4, Table 5). Conversely, although the limit warnings of $N_1$ and $N_2$ are satisfied, $N_{event-co}$ may still exceed $N_{event-s}$. In this case, $N_{event-s}$ is necessary to be controlled to satisfy the condition that $R_{rs}$ is less than 1, while maintaining $N_1$ and $N_2$. Moreover, we note that scenarios in which the value of $N_{event-s}$ is greater than $N_{event-co}$ occur mainly under conditions of longer duration, speaking, poor ACH, and variants (e.g., Delta and Omicron). Thus, a second modification of $N_{event-s}$ is performed, and the minimum between the $N_{event-co}$ and $N_{event-s}$ is selected as the limit warning of $N_{event}$.

As for different strain variants, the influence ACH on $I{R}_{rs}$ and $R_{rs}$ is analyzed in Fig. 9 . The light red color indicates $R_{rs}=1$, and $R_{rs}$ increases as the red deepens. The assumption is made that each circumstance represented by a rectangular cell is an equiprobable event. For the Normal strain, the proportion of blue cells in buses, subways, and high speed trains was 91%, 84%, and 83%, respectively. For Delta, the proportion of blue cells was 13%, 9%, and 10%, respectively. For Omicron, the proportion of blue cells was 7%, 0%, and 5%, respectively. In other words, ${IR}_{rs}$ is acceptable in UPT for Normal, ensuring that $R_{rs}$ is less than 1. However, for Delta and Omicron, $R_{rs}>1$ may still occur despite a short exposure duration and high ventilation. $I{R}_{rs}$ will increase dramatically for Delta and Omicron, which may lead to widespread and even SSEs.

Fig. 9.

$I{R}_{rs}$ versus exposure duration and ACH in (a) buses, (b) subways, (c) high speed trains.

When ACH increased by 5 h⁻¹, the average mitigation level of $I{R}_{rs}$ for buses were 1.6-folds and 1.4-folds higher than for subways and high speed trains, respectively. Therefore, buses have a greater potential to reduce $I{R}_{rs}$ by increasing ACH, as indicated by Fig. 6. The proportion below the typical ventilation rate in buses was the greatest and similar to subways, roughly 5-folds higher than high speed trains. Based on $I{R}_{cp01}$ and $I{R}_{cp12}$ (Section 3.3), $I{R}_{rs}$ (Section 3.4), $N_1$, $N_2$, and $N_{event}$ (Table 1), total R for a specific circumstance could be obtained under the minimum typical value of ACH (5 h⁻¹ for buses; 10 h⁻¹ for subways; 5 h⁻¹ for trains). To obtain the maximum R for Normal, Delta, and Omicron, it is assumed that the respiratory activity of the index case is speaking. Furthermore, two scenarios of exposure duration were assumed, including the minimum/maximum exposure duration (i.e., 0.1 h/1.5 h for buses, 0.1 h/1.5 h for subways, and 0.2 h/4.0 h for high speed trains, respectively), and the average R was also calculated per exposure interval. Results are shown in Fig. 10 .

Fig. 10.

The calculated total R with (a) the minimum exposure duration, (b) the maximum exposure duration, and (c) the average exposure duration.

As seen in Fig. 10, the total $R$ of buses was 0.8-folds (average, ranging from 0.5 to 1.0-folds) higher than subways. Similarly, the total $R$ of high speed trains was 0.6-folds (average, ranging from 0.5 to 0.8-folds) lower than subways. The overall risk level of subways was higher than buses and high speed trains. Compared with the Normal strain, the total $R$ caused by Omicron was 5.5-folds, 4.9-folds, and 4.4-folds higher for buses, subways, and high speed trains, respectively. Moreover, R caused by Delta increased by 3.8-folds for buses, 3.2-folds for subways, and 3.0-folds for high speed trains higher than Normal, respectively. Although improving ventilation (Section 3.3, Section 3.4) and maintaining social distance (Section 3.2) are both useful, they are not enough to prevent SSEs in high-occupancy UPT considering the high basic reproduction number. Therefore, additional measures such as wearing a mask should be taken, which will be evaluated quantitatively in the following subsection.

3.4. Influence of wearing surgical masks on $I{R}_{rs}$

$I{R}_{rs}$ can be obtained based on Eqs. (9), (10) and data in Table 3. To facilitate the discussion in the later sections, we have analyzed two common mask-wearing scenarios, namely the index case-wearing scenario (where only the index case wears a surgical mask) and the both-wearing scenario (where both the index case and susceptible individuals wear a surgical mask). For these two scenarios, the corresponding results of $I{R}_{rs}$ are illustrated in Fig. 11 (a1, b1, c1) and Fig. 11 (a2, b2, c2). Compared with the results in Figs. 8 and 9, there was a significant reduction effect on $I{R}_{rs}$ when wearing masks. For index case-wearing scenario, $I{R}_{rs}$ was reduced on average by 81.6% for buses, 80.3% for subways, and 77.8% for high speed trains, respectively, which indicates that the reduction level maintains a high consistency. For buses in Fig. 11 (a1), the average mitigation level of $I{R}_{rs}$ was 1.5-folds, 1.9-folds, and 2.0-folds than increasing ACH, respectively. For buses and high speed trains, when the index case was breathing, the exposure duration when $R=1$ was 1.4 h and 2.6 h in Fig. 11 (a1, c1). Moreover, the protection time calculated by Ref. [62] was 1.3 h and 2.8 h, respectively, which agreed with our results.

Fig. 11.

$I{R}_{rs}$ versus exposure duration in typical scenarios, including index case-wearing scenario: (a1) buses, (b1) subways, (c1) high speed trains, and both wearing scenario: (a2) buses, (b2) subways, (c2) high speed trains.

It can be found from Fig. 11 (a2, b2, c2) that the average mitigation effect is greater for the both-wearing scenario, which was 3.6-folds on average for the index case-wearing scenario. Wearing masks properly is a more effective measure compared to solely increasing ventilation. For the both-wearing scenario, $R\ge 1$ may appear only during the minimum typical ACH for a longer exposure duration. However, there is also the possibility of $R\ge 1$ when susceptible individuals stay for more than 1.3 h in subways (ACH = 15 h⁻¹). It is recommended that all individuals wear a mask to reduce the higher risks generated by speaking, coughing, or overstaying. In general, $I{R}_{rs}$ of the UPT are acceptable ($I{R}_{rs}<1$) for the both-wearing scenario although under the minimum typical values of ACH (5 h⁻¹ for buses; 10 h⁻¹ for subways; 5 h⁻¹ for high speed trains).

4. Discussion

According to the video recording, most passengers were wearing surgical masks, as shown in Fig. 2d of the snapshots in crowded circumstances. Table 3 suggests that the leakage rate of surgical masks was greater than that of FFP2 masks. To estimate conservatively the effect of wearing a mask on risk mitigation, the protective performance of surgical masks was analyzed typically. Different from the 50% roughly considered [43,63], the filtration efficiency of the mask was reasonably assessed in this paper, according to the initial particle size distribution under actual respiratory activity and the leakage rate of the corresponding particle size. Based on the ratio of the particle's volume inside and outside the mask and the assumption of the same viral concentration contained in different particle sizes [50,51], modified mask filtration efficiencies (${TIL}_c$ and ${TOL}_c$) were applied.

The fitting of masks to a person's face also significantly affects the total particle leakage rate, and ultimately lowers the protective effect [62]. Wearing a mask for a long time tends to cause some physical symptoms [64], which is often considered as an important influence on face fitting. To minimize discomfort [64], found that wearing a mask for more than 2 h was not recommended. Subsequently, to reduce the thermal discomfort caused by masks, there is a high probability that passengers wear them irregularly, leaving their nose or mouth bare outside a mask. Unfortunately, passengers may even directly remove the mask, especially passengers with anxiety or asthma [65]. In addition, eating and drinking non-alcoholic beverages are permitted on high speed trains due to longer travel [66]. For buses and subways, eating is banned but drinking briefly is accepted, which is not strongly enforced and is mostly ignored. This suggests that the likelihood of removing masks is higher in high speed trains compared to buses and subways [67]. found that the particle filtration efficiency (PFE) and bacterial filtration efficiency (BFE) of the masks decreased as the actual wearing time increased. In this paper, we did not consider the influence of mask-wearing time on its PFE. It is assumed that the mask is newly used or the total duration of reuse is relatively short, and the filter structure is not damaged.

Basic reproduction number ($R_o$) may vary in infectious periods and different outbreaking regions [68], which may affect the value of $f$. Based on the study by Ref. [43]; $E{R}_q$ was obtained for three SARS-CoV-2 variants by Ref. [68]. Furthermore, combining with the study by Ref. [25]; the value of $f$ ranges from 6.5 to 19.5 for Delta and 15.1 to 48.5 for Omicron. In this study, the $f$ value of 10.8 for Delta ($R_o$ = 6.2) and 30.1 for Omicron ($R_o$ = 9.5) were used to provide an averaged input for the Monte Carlo simulations [25]. The influence of different values of $R_o$ (e.g., 5.1 or 8.0 for Delta, 7.2 or 12 for Omicron [68]) on the infection risk was not analyzed currently. In the future, the infection risk of built environments can be obtained according to the actual $R_o$ in an urban or country. In addition to the virus species or different variants, other variables such as passenger density and ventilation also greatly affect the reproduction number. $N_1$, $N_2$, $N_{rs}$, and the location of the index case varies from case to case. However, different occupancy conditions should also be attended, e.g. full seat condition, where the distribution characteristics of the crowd can be crucial for the particle transport [37]. The current TJWR model applied in the UPT does not address the implications of airflow patterns, which may normally be obtained with CFD tools.

Opening windows randomly in the bus may affect the non-uniform mixing of virus-laden aerosols or droplets at the room scale. However, to simplify this uncertainty problem, we assume that the air is perfectly mixed for the room-scale. Moreover, the assumption of a deposition rate of 0.24 h⁻¹ is likely invalid within the UPT compartment environment. The deposition rate is in theory size-dependent [46] but not treated in a size-resolved manner in this study. For full load conditions of the UPT, particles may also deposit more rapidly onto clothing and bare skin surfaces rather than solely on the floor. There is a compromise between accuracy and efficiency for risk assessments in this study. The above limitations can be investigated in our future study.

To simplify the problem, high-occupancy scenarios in UPT are chosen (full load condition), and the passenger's distribution is considered steady to evaluate the total R comprehensively. However, provided that a social distance of greater than 2 m is guaranteed or that masks are worn by all, ACH is subsequently adjusted according to the actual passenger number and location distribution. According to Fig. 8 ventilation is efficient evidence to reduce room-scale risks. However, Fig. 5 shows that ACH continuously fluctuates within an interval versus the exposure duration and is not stable. The impact of time-varying ACH on the risks was not analyzed, and only typical values of ACH considered to be stable were selected. In addition, it is challenging to increase ventilation, which needs significant investment in the ventilation system and additional energy consumption [69]. Therefore, finding the optimal balance point between multi-scale infection risk and energy consumption can be crucial for transit operators of UPT [70,71]. The one-size-fits-all strategy cannot be adopted. According to the infection risks under different scenarios of UPT obtained from our simulations, the governors can guarantee that the UPT runs more efficiently, and develop appropriate energy-efficient strategies for the UPT. Moreover, based on the actual distribution of $N_1$, $N_2$, and $N_{rs}$, respiratory parameters, ACH, and viral load data ($E{R}_q$), the individual's infection risk can be detected in real-time. Spatial-scale based upper limit warnings at the multi-scale (i.e., $N_1$, $N_2$, and $N_{event}$) can be proposed to guide citizens to rationalize their duration and social distance.

5. Conclusion

The COVID-19 pandemic poses significant challenges to the safety of the UPT environment worldwide. Based on field measurements in Hangzhou, China, during pandemic periods (measured dates ranging from February to July 2021), the average CO₂ concentration in the peak periods was 2.2-folds and 1.3-folds higher than in the off-peak periods for buses and subways respectively. In high speed trains, the CO₂ concentration exceeded 2000 ppm with an average value of 1298 ppm. According to the number of passengers, ACH was 9 h⁻¹ for buses (average, ranging from 2 h⁻¹ to 20 h⁻¹), 16 h⁻¹ for subways (average, ranging from 8 h⁻¹ to 22 h⁻¹), and 8 h⁻¹ for high speed trains (average, ranging from 4 h⁻¹ to 11 h⁻¹). The proportion of poor ventilation was 75% for buses, 83% for subways, and 25% for high speed trains, respectively. Infection risk thresholds at multi-scales (i.e., short-range 1, 2, and room-scale) were obtained (7.1%, 4.2%, and 0.78% for buses; 6.3%, 3.4%, and 0.23% for subways; 25.0%, 7.1%, and 0.62% for high speed railways). Similarly, based on the TJWR model, to obtain a guideline exposure duration, time-scale based exposure thresholds (i.e., ET and ET_i) were calculated for different scenarios. Results indicate that poor ventilation, the larger transmission enhancement coefficient (f) for SARS-CoV-2 variants, and speaking all cause shorter ET values and a greater time interval for ET_i. That is, in the UPT, being infected can occur within as little as 0.1 h.

Enhancing ventilation has a limited effect on reducing average risks at the short-range of the UPT, only less than 10%. By maintaining a social distance greater than 2 m, $N_1$ and $N_2$ can be reduced, thereby decreasing $R_{cp01}$ and $R_{cp12}$. Based on the real-time compartment environments, spatial-scale based upper limit warnings of the multi-scale (i.e., $N_1$, $N_2$, and $N_{event}$) were obtained, which can be as guiding principles for transit operators to control occupancy rates. At the room-scale ($R_{rs}$), when increasing ACH, the average reduction level of the UPT can be more than 50%. According to three typical exposure durations, different SARS-CoV-2 variants, and actual values of ACH, the total R of buses and high speed trains were 0.8-folds (average, ranging from 0.5 to 1.0-folds) and 0.6-folds (average, ranging from 0.5 to 0.8-folds) lower than subways, respectively, which indicates that the overall risk of subways is a cause for concern. Compared with increasing ACH, the average reduction effect in buses, subways, and trains was 1.5-folds, 1.9-folds, and 2.0-folds for the index case-wearing scenario. For the both-wearing scenario, the reduction effect was 3.6-folds more than the index case-wearing scenario. Therefore, mask wearing provides the greatest protection against infection in the face of long exposure duration to the omicron epidemic.

CRediT authorship contribution statement

Yinshuai Feng: Writing – original draft, Validation, Software, Methodology, Investigation, Conceptualization. Yan Zhang: Writing – review & editing, Visualization, Resources, Formal analysis. Xiaotian Ding: Writing – review & editing, Visualization, Resources, Formal analysis. Yifan Fan: Writing – review & editing, Validation, Supervision, Resources, Formal analysis. Jian Ge: Writing – review & editing, Supervision, Resources, Formal analysis.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

Data will be made available on request.