Introduction

Enclosed environments are among the most common venues that severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is transmitted (Qian et al. 2021). Cumulative evidence showed that airborne transmission is associated with micron-scale aerosol droplets that could inevitably occur in confined spaces (Bazant and Bush 2021; Jayaweera et al. 2020; Mittal et al. 2020; Morawska and Milton 2020; Zhang et al. 2020). Among all kinds of built environments, increasing studies have found that hospitals could be one of the hotbeds cultivating super spreaders due to the higher risks resulting from intensive contacts of healthcare workers with infectors and congregations of inpatients, outpatients, and visitors from various places (Huang et al. 2022; Illingworth et al. 2021; Wei et al. 2020). However, in addition to source controls (e.g., social distancing and wearing of face mask), there has been limited knowledge in other mitigation measures such as applications of engineering controls (e.g., air supply rate and room volume) on disease transmissions in hospitals or healthcare facilities (Allen and Ibrahim 2021).

The main routes for SARS-CoV-2 transmission in hospitals are suggested to be direct transfer of respiratory droplets (e.g., coughing, sneezing, saliva, handling mucous membranes from mouth, nose, and eyes) (Lu et al. 2020; To et al. 2020) or indirect transfer through contaminated surfaces where virus remains for several days (Doremalen et al. 2020). Between the two transmission routes, airborne transmission through inhalation of aerosol droplets exhaled by an infected person is now thought to be the primary transmission route of SARS-CoV-2 (Bazant and Bush 2021). Therefore, effective containments on disease transmissions intraunits/interunits of hospital buildings are highly recommended. It is also of great essence to clearly understand the role or impacts of indoor settings on the transmissibility of SARS-CoV-2.

Although there have been guidelines or standards covering air exchange rates in various kinds of spaces or healthcare facilities (AIA 2001; ASHRAE 2020; TAHPI 2015), these standards may not be applicable for disease containments when more patients/visitors are present in hospitals or higher staying durations are required. Also, due to the limited knowledge in practical control measures on indoor transmissions of SARS-CoV-2, a mechanistic approach is needed to deeply evaluate influences of ventilations, exposure time, or indoor populations for better prevention of potential disease transmissions in certain aerosol microenvironments.

To address this approach, we adopted the Wells-Riley model as the mechanistic approach due to its linking with various adjustable indoor conditions and potentiality in design and indoor transmission assessments of healthcare buildings. The inhaled-exhaled air dynamics-based Wells-Riley model has successfully treated airborne transmission of infectious diseases (Guo et al. 2021; Rudnick and Milton 2003). To more straightforwardly explore the associations of various conditions of indoor setting with the basic reproduction number (R0) (the average number of secondary infections produced by an infected individual in a susceptible host population), a modified Wells–Riley equation with appropriate mathematical manipulations were applied in indoor transmission modeling (Chen et al. 2006). To take the intrinsic limitation of the model into account, we considered the most conservative scenario with one infector and lower ranges of physiological parameters in parameterizations as baseline evaluations for R0 estimations. Although there are several limitations in the Wells-Riley model, the approach along with modified ones generally make valid arguments for airborne infectious disease transmission and agree in their predictions of concentration profiles and infection risk (Cheng and Liao 2013; Foster and Kinzel 2021; Qian et al. 2009). Furtherly, we also performed a case study investigating probabilistic-based R0s with different scenarios of inhalation rates in the two Wuhan (Fangcang/Renmin) hospitals by adopting the field data of Liu et al. (2020). Apart from field estimations, functional spaces in healthcare facilities with different role delineation of levels (RDLs) were also performed for general estimations. The RDLs refer to a level of service describing the complexity of clinical activities undertaken by that service. The level is determined by the presence of medical, nursing and other healthcare personnel holding compatible with the defined level of service (TAHPI 2015). The emergency unit with typical volumes for functional rooms from RDL1 to RDL6 defined in TAHPI (2015) was exemplified as a general illustration for healthcare buildings to explore the impacts of air supply rates, indoor population numbers, or exposure time on controlled reproduction number (RC) (the average number of new individuals infected by an infector with SARS-CoV-2 given the current control measures) to provide theoretically sound prevention strategies on airborne transmissions. Finally, sensitivity analyses were performed to elucidate the most remarkable parameters contributing to space-specific airborne SARS-CoV-2 transmissions.

Materials and methods

Study data

Field data of interior designs of two Wuhan (Fangcang/Renmin) hospitals were adapted from published literature (Liu et al. 2020). Specifically, the floor plan of Fangcang shelter hospital including three zones (A, B, and C) and a mobile toilet (portable toilet that can be moved around) near the rear gate are schematized based on Liu et al. (2021) (Fig. 2). The shelter hospital was built in a large space located in the Wuhan Cultural Centre with adequate ventilations and 1400 beds in the three Zone areas, in which the Protective Apparel Removal Room (PARR) refers to a functional room to remove personal protective equipment by medical staff (Liu et al. 2021).

For general considerations of indoor settings in healthcare facilities for the following simulations of indoor transmissions, averaged room volumes in hospitals with different service levels from RDL1 to RDL6 were obtained from TAHPI (2015) (Supplementary Table S1). Among all functional units, only the emergency unit was exemplified for simulations of indoor transmissions in different indoor scenarios (e.g., exposure time, indoor population number, or air supply rate).

Indoor transmission model and study design

The Wells-Riley model was used to describe airborne transmission and assess potential infection risks in enclosed environments. The infection risk can be evaluated with the Wells-Riley mathematical equation as follows,

$$P=\frac{D}{S}=1-\mathrm{exp}\left\{\frac{-iqpt}{Q}\left\{1-\frac{V}{Qt}\left[1-\mathrm{exp}\left(\frac{-Qt}{V}\right)\right]\right\}\right\},$$
(1)

where D is the number of infected ones, S is the number susceptible subjects, i is the number of infectors, q is the quantum generation rate by an infectious individual (quanta h−1), p is the inhalation rate per person (m3 h−1), t is the total exposure time (staying duration) (h), Q is the fresh air supply rate to remove infectious aerosol particles in an enclosed space (m3 h−1), and V is the room volume (m3).

With appropriate mathematical manipulations from Eq. (1) based on previous studies (Chen et al. 2006; Rudnick and Milton 2003), indoor R0 for an airborne infection could be estimated by the Wells-Riley model based on characteristics of building settings along with population physiology,

$${R}_{0}=\left(n-1\right)\left\{1-\mathrm{exp}\left\{\frac{-qpt}{Q}\left[1-\frac{V}{Qt}\left(1-\mathrm{exp}\left(\frac{-Qt}{V}\right)\right)\right]\right\}\right\},$$
(2)

where n is the number of total populations indoors, n − 1 stands for the assumption that there are 1 infector, and thus, n − 1 susceptible individuals at an initial respiratory infection condition.

Since the modified Wells–Riley model assumes that there would be one infector indoors, we considered a relatively safe indoor exposure scenario as the most conservative evaluation for R0 with one infector, normal quanta generation rate (< 100 quanta h−1), and resting as the activity level with the basic requirements for room volumes and ventilations in healthcare buildings based on previous literature (ASHRAE 2020; TAHPI 2015). The consideration for using the most conservative scenario could give a general realization for the baseline of R0 if only one infector is considered in the indoor environments, and higher R0 would be expected if more infectors, higher quanta generation numbers, or inhalation rates are applied with the same indoor conditions.

Mode parameterizations and implementations

Specifically, the Vs were derived by adopting the basic requirements for room spaces from RDL1 to RDL6 in healthcare facilities (TAHPI 2015) (Supplementary Table S1). Qs was probabilistically derived based on the basic requirements of air change per hour (ACH) in health care facilities (ASHRAE 2020) (Supplementary Tables S2-S4), where the ACHs were estimated in three space categories of inpatient, outpatient, and residential health or care, and support-specific (Supplementary Fig. S1a-c; Supplementary Table S5). Basic requirements of ACH corresponding to each functional areas in the two Wuhan (Fangcang/Renmin) hospitals were compiled (Supplementary Table S6). For the exemplified emergency unit in healthcare facilities, derived requirements for room volumes corresponding to basic ACH rates were also listed (Supplementary Table S7).

The q was probabilistically estimated based on results derived from a reproductive number-based fitting approach (Dai and Zhao 2020), by assuming that occurrence of high quanta emission rate (> 100 quanta h−1) is relatively unlikely in healthcare facilities (Buonanno et al. 2020) (Supplementary Fig. S1d). For inhalation rate, since there are high variabilities among the five different activity levels (0.49, 0.54, 1.38. 2.35, and 3.30 m3 h−1 for resting, standing, light exercise, moderate exercise, and heavy exercise, respectively) averaged between males and females (Adams 1993; Buonanno et al. 2020), the probability distribution of p was derived by considering all activity levels (Supplementary Fig. S1e).

The R0 estimates were evaluated in the three inpatient areas (Zones A, B, and C workstations) of two Wuhan (Fangcang/Renmin) hospitals with basic requirements of ACHs and assumed indoor populations and exposure time referred from Liu et al. (2021) (Supplementary Tables S6). There were two scenarios implemented for R0 estimations in the three inpatient areas of two Wuhan hospitals by considering: (i) variabilities in inhalation rates with inclusions of the five different activity levels (Supplementary Figs. S1e) and (ii) the inhalation rate in resting scenario as a baseline evaluation for R0 estimates. For the R0 simulations in different functional spaces of the two Wuhan hospitals and the exemplified emergency unit, space-specific R0s were dynamically estimated with different exposure time and indoor population numbers based on the basic requirements of room volumes and ACHs (Supplementary Table S6). Interactions of R0 − exposure time (t) − population number (n) were constructed by using the inhalation rate in resting scenario as a baseline evaluation to provide the most conservative estimations of R0 in planning COVID-19 control measures when applying the scenario of one infector and the lowest inhalation rate in indoor spaces in control models.

COVID-19 control models

Here, we proposed three RC-control models that only require data on basic requirements of ACHs and room volumes and any designated indoor population numbers or exposure time. The emergency unit in general health care buildings from RDL1–RDL6 was used to explore associations of RC changes with different control measures by using the basic design requirements for room volumes and ACHs in the 8 categorized functional areas (entry/reception/waiting, triage, resuscitation/treatment area, fast track-primary care/consulting, support areas, paediatric assessment/short stay, mental health/behavioural assessment, and staff areas) (Supplementary Table S7).

The first controlled model was intuitively based on the Wells-Riley model as follows,

$${R}_{c}=\left({n}_{c}-1\right)\left\{1-\mathrm{exp}\left\{\frac{-{qpt}_{c}}{Q}\left[1-\frac{V}{{Qt}_{c}}\left(1-\mathrm{exp}\left(\frac{-{Qt}_{c}}{V}\right)\right)\right]\right\}\right\},$$
(3)

where nc is the increments of controlled number of persons, and tc is the controlled total exposure time. The constructed control lines of nc − tc lay out a practical metric for examining qualitatively and quantitatively the efficacy of containment on the spread of COVID-19 based on area under the contour lines of RC estimates: RC < 1, the outbreak will be contained eventually; RC > 1, however, additional interventions should be intervened.

In the second model, we aimed to offer a strategy to adjust both ACH and indoor population number simultaneously for COVID-19 containment. The RCs were evaluated by adjusting various controlled ACHs (ACHC) and tc with a threshold indoor population number (nc,t) that was estimated when R0 = 1 and tc = 1 h with basic requirements of ACHs and room volumes as the following equation (ASHRAE 2020; TAHPI 2015),

$${R}_{c}=\left({n}_{c,t}-1\right)\left\{1-\mathrm{exp}\left\{\frac{-{qpt}_{c}}{{Q}_{c}}\left[1-\frac{V}{{{Q}_{c}t}_{c}}\left(1-\mathrm{exp}\left(\frac{-{{Q}_{c}t}_{c}}{V}\right)\right)\right]\right\}\right\}.$$
(4)

Moreover, to adapt to the scenario that several buildings have limited resources to adjust air supply systems, we established the third model to estimate RC in the condition that controlled exposure time (tc) is higher than 1 h and controlled indoor populations (nc) are higher than the second control model-derived nc,t estimates with the basic requirements of ACHs (Supplementary Tables S6-S7) as follow,

$${R}_{c}=\left({n}_{c}-1\right)\left\{1-\mathrm{exp}\left\{\frac{-{qpt}_{c}}{Q}\left[1-\frac{V}{{Qt}_{c}}\left(1-\mathrm{exp}\left(\frac{-{Qt}_{c}}{V}\right)\right)\right]\right\}\right\}.$$
(5)

Therefore, to investigate airborne transmissions of SARS-CoV-2 and propose practical strategies for COVID-19 containments in two Wuhan hospitals and general healthcare facilities, the study framework was designed as (i) data collections of interior settings of two Wuhan hospitals with basic requirements for ACH and room volumes in healthcare facilities (Fig. 1a); (ii) applications of the Wells-Riley model based on conservative parameterizations of quantum generation number, inhalation rate, room volume, air supply rate, and indoor population number (Fig. 1b); (iii) model implementations of dynamic R0 estimates with various exposure time and peoples and explorations of the most sensitive parameters by performing sensitivity analyses (Fig. 1c); and (iv) provisions of strategies for COVID-19 containments based on three RC-control models constructed by the relationships among population number, exposure time, and ACH (Fig. 1d).

Fig. 1
figure 1

Overall research framework illustrating the Wells-Riley modelling and containment strategies for two Wuhan hospitals/healthcare facilities. (a) Data collection, (b) Wells-Riley model, (c) model implementation, and (d) indoor COVID-19 infection control models

Full size image

Uncertainty and sensitivity analyses

Uncertainty analyses performed for estimating key human physiological/engineering parameters including room volumes, ACH, quantum generation number, and inhalation rate in the Wells-Riley model were implemented with 100,000 Monte Carlo (MC) simulations to obtain geometric means (gms), and geometric standard deviations (gsds) in lognormal (LN) functions (LN(gm, gsd)) with the Crystal Ball software (Version 11.1.2.4, Oracle Corporation, Redwood Shores, CA, USA). Data visualizations such as 3-dimensional scatter, contour, and bubble plots were generated by using the language R (Version 4.1.3, The R Foundation for Statistical Computing). Sensitivity analyses were performed by adjusting each parameter with 0.1 × or 10 × ranges to evaluate the overall contributions of each physiological or engineering parameter to R0 in each functional room of the two Wuhan hospitals or the emergency unit in healthcare facilities as: (R0 (Rc) estimated from 0.1 × or 10 × -adjusted parameter − R0 (Rc) estimated from 1 × parameter)/0.1 × or 10 × -adjusted parameter.

Results

Parameterizations in the Wells-Riley model

Essential physiological or engineering parameters applied in the indoor transmission model were probabilistically pre-estimated and derived before R0 estimations. Specifically, distributions of ACH were estimated with LN functions as LN (7.05, 3.04), LN (7.90, 4.40), and LN (7.27, 3.75) in for inpatient, outpatient, and residential health or care, and support-specific spaces, respectively (Supplementary Figs.S1a-c). The distribution of q (14 − 48 quanta h−1) adopted from Dai and Zhao (2020) was estimated as LN (25.90, 1.45) (Supplementary Fig. S1d). The inhalation rate was probabilistically estimated as LN (1.29, 1.95) by applying high uncertainties in the five activity levels (Supplementary Fig. S1e).

R0 in patient areas of Fangcang hospital

We estimated R0 in Zones A, B, and C of Fangcang hospital with two scenarios by taking variabilities of inhalation rate (Supplementary Fig. S1e) and the inhalation rate in resting level based on conditions of 100 or 200 persons and exposure time of 20 h indoors (Supplementary Table S7). The estimated ranges of ACH of patient care areas and clinical support spaces (LN(7.05 h−1, 3.04) – LN(7.90 h−1, 4.40)) were applied in R0 estimations (Supplementary Fig. S1a, b, c). Results showed that the R0 estimates are consistently higher when applying the inhalation rate with variabilities (Fig. 1a, c, e, g, i, k). Among the three zones, Zone B with the smallest volume (V = 2000 m3) exhibited the highest R0s of LN (5.21, 2.74) and LN (1.85, 2.67) when 100 people indoors with higher (considering activity variabilities) and lower (resting scenario) inhalation rates, respectively (Fig. 2c, d). Also, the R0 estimations in Zone A and C (V = 5000 m3) have closed results in the same conditions of inhalation rate or indoor population numbers (Fig. 2a, b, e, f, g, h, k, l).

Fig. 2
figure 2

Basic reproduction numbers (R0s) estimates as the lognormal (LN) distribution (LN(gm, gsd)) in Zones A, B, and C of patient areas of the Fangcang hospital under conditions of total exposure time of 20 h and indoor population of 100 when a, c, e taking variabilities in inhalation rate for consideration and b, d, f using the inhalation rate in resting level or indoor population of 200 when g, i, k taking variabilities in inhalation rate for consideration and h, j, l using the inhalation rate in resting level

Full size image

R0 estimations with dynamic exposure time and indoor population number

Our results showed that among the three patient areas, Zone B still exhibited the highest R0s when compared to those of Zones A and C in the same indoor conditions, in that R0s exceed 1 when there are 400 people staying over 3 h and 500 people over 6 h in Zones B and A/C, respectively (Fig. 3a, b, c). Additionally, the passageway for medical staff (Renmin hospital) had the highest R0s (Fig. 3k), followed by medical staff’s office (Fig. 3f),; intensive/coronary care unit and Ward Zone 16 (Fig. 3j); PARR of Zones A, B, and C (Fig. 3d); dining room for medical staff (Fig. 3l) or university office doorside (Fig. 3m); warehouse (Fig. 3h); Fangcang hospital pharmacy (Fig. 3i); university hospital outpatient hall (Fig. 3n); staff change room (Fig. 3e); and meeting room (Fig. 3g). Generally, the smaller the room volume, the higher the R0s (Supplementary Table S7).

Fig. 3
figure 3figure 3

R0 − exposure time (t) − indoor population numbers (n) interactions in a Zone A, b Zone B, and c Zone C workstations; d Protective Apparel Removal Room (PARR) of Zone A/B/C, e staff change room, f medical staff’s office, g meeting room, h warehouse, and i pharmacy of the Fangcang hospital. And j Intensive Care Unit (ICU), Coronary Care Unit (CCU), and Ward Zone 16, and k Passageway for Medical Staff, l Dining Room for Medical Staff, m University Office Doorside, and n University Hospital Outpatient Hall of the Renmin hospital

Full size image

For sensitivity analyses, results indicated that inhalation rate (p) has the most significant effect on R0s in all room types, followed by air supply rate (Q), exposure time (t), q, numbers of population (n), and room volume (V) (Supplementary Fig. S2). Results also revealed that the smaller the V, the higher the effects of each physiological/engineering parameter on R0 (Supplementary Fig. S2).

RC simulations with dynamic exposure time and indoor population number in emergency unit

In the first RC-control model, we used representative functional rooms to explore associations of changes of ACHs and indoor population numbers with RC estimates in different functional rooms of the emergency unit (Supplementary Fig. S3). Overall, the top three areas with the highest standards of indoor population number (nc) based on the same condition of exposure time (tc = 2 h) at RC < 1 were bay-handwashing (support areas) (nc = 5) (Fig. 4D), triage-nurse (triage) (nc = 7) areas (Fig. 4e), and reception (entry/reception/waiting) (nc = 14) (Fig. 4a). In contrast, area with the loosest standard was patient bay-resuscitation area (resuscitation trauma) (nc = 80) (Fig. 4b).

Fig. 4
figure 4

Contour plots describing RCs with various controlled total exposure time (tc, h) and controlled population number (nc) under basic requirements of ventilation rate and room volume in functional room of a reception (entry/reception/waiting), b patient bay-resuscitation (resuscitation/treatment area), c procedure room (resuscitation/treatment area), d bay-handwashing (support areas), e triage-nurse (triage), f consult room (fast track-primary care/consulting), g staff room (staff areas), and h patient bay-non acute treatment (paediatric assessment/short stay) in the emergency unit. Red arrows indicate path of travel. Only representative functional rooms were selected to present the simulation results for the control measure as described in (Supplementary Table S7)

Full size image

On the other hand, our simulated functional space-specific RC dynamics showed that rooms with the most rigorous standard on COVID-19 containment in entry/reception/waiting, triage, resuscitation/treatment area, fast track-primary care/consulting, support areas, paediatric assessment/short stay, and staff areas were bay-wheelchair park, nurse triage, shower-patient, bay-handwashing, bay-pathology, store-equipment/general, and toilet-staff, respectively (Supplementary Fig. S3).

Fixed nc,t-based control measure in emergency unit

The functional room-specific nc,ts were derived with the condition of RCs = 1 and tc = 1 h with basic requirement of room volumes. Our results showed that bay-handwashing (support area) had the lowest nc,t given a minimum requirement of room volume (Vm) (nc,t = 10, Vm = 12 m3) (Fig. 5d), followed by triage-nurse (triage) (nc,t = 15, Vm = 20 m3) (Fig. 5e), reception area (entry/reception/waiting) (nc,t = 30, Vm = 44 m3) (Fig. 5a), staff room (offices meeting rooms/staff support) (nc,t = 40, Vm = 54 m3) (Fig. 5f), procedure room (procedures) (nc,t = 55, Vm = 81 m3) (Fig. 5c), consult room (adult fast track) (nc,t = 80, Vm = 113 m3) (Fig. 5g), patient bay-non acute treatment (paediatric assessment or acute/non-acute observation) (nc,t = 90, Vm = 135 m3) (Fig. 5h), and patient bay-resuscitation area (resuscitation trauma) (nc,t = 120, Vm = 180 m3) (Fig. 5b).

Fig. 5
figure 5

Bubble plots showing control measures on controlled ACH (ACHc) with various controlled total exposure time (tc) based on estimated threshold indoor population number (nc,t) in a reception (entry/reception/waiting), b patient bay-resuscitation (resuscitation/treatment area), c procedure room (resuscitation/treatment area), d bay-handwashing (support areas), e triage-nurse (triage), f consult room (fast track-primary care/consulting), g staff room (staff areas), and h patient bay-non acute treatment (paediatric assessment/short stay) of the emergency unit. Red arrows indicate path of travel. Only representative functional rooms were selected to present the simulation results for the control measure as described in (Supplementary Table S7)

Full size image

In the second RC-control approach, not surprisingly, we found an overall trend that the higher the ACH, the lower the RC estimate. Results also indicated that COVID-19 could be reduced by adjusting ACH, to higher than 7 h−1 of all functional rooms in the emergency unit with nc,t ≤ 10 and tc = 1 h (Fig. 5). However, when tc increased to an extreme level of 8 h (in this study), ACH should also be increased to a much higher value as follows: bay-handwashing (support area, 40 h−1), triage- nurse (triage, 68 h−1), reception area (entry/reception/waiting, 66 h−1), staff room (offices meeting rooms/staff support, 62 h−1), procedure room (procedures, 48 h−1), consult room (adult fast track, 66 h−1), patient bay-non acute treatment (paediatric assessment or acute/non-acute observation, 54 h−1), and patient bay-resuscitation area (resuscitation trauma, 67 h−1) (Fig. 5).

Fixed air supply rate-based control measure in emergency unit

In the third RC-control model (Fig. 6), RCs were estimated in the condition of tc > 1 h and nc > nc,t with basic air supply rate (Qc) in each functional room. Results showed that in the most extreme scenario of exposure time in this study (tc = 8 h), RCs could be as high as 33 in bay-handwashing (support area) (Fig. 6d), followed by 18 in triage-nurse (triage) (Fig. 6e), 13 in reception area (reception/administration) (Fig. 6a), 11 in staff room (offices meeting rooms/staff support) (Fig. 6f), 8 in procedure room (procedures) (Fig. 6c), 6 in consult room (adult fast track) (Fig. 6g), and 4 in both patient bay-non acute treatment (paediatric assessment or acute/non-acute observation) (Fig. 6h) and patient bay-resuscitation area (resuscitation trauma) (Fig. 6b) when nc = 50.

Fig. 6
figure 6

Bubble plots showing control measures on controlled population number (nc) with various controlled total exposure time (tc) based on basic requirements of ventilation rate and room volume in a reception (entry/reception/waiting), b patient bay-resuscitation (resuscitation/treatment area), c procedure room (resuscitation/treatment area), d bay-handwashing (support areas), e triage-nurse (triage), f consult room (fast track-primary care/consulting), g staff room (staff areas), and h patient bay-non acute treatment (paediatric assessment/short stay) of the emergency unit. Red arrows indicate path of travel. Only representative functional rooms were selected to present the simulation results for the control measure as described in (Supplementary Table S7)

Full size image

Similar to the results from two Wuhan hospitals, sensitivities of each physiological/engineering parameter on RCs in the emergency unit depend significantly on room volumes (Supplementary Fig. S4). Among all parameters, inhalation rate p also has the most significant effects on room type-specific RC, followed by tc, Vc, Qc, nc, and q (Supplementary Fig. S4).

Discussion

Role of indoor transmission in COVID-19 pandemics

There has been a growing body of evidence that airborne transmission is associated with the spread of COVID-19, especially in poorly ventilated built environments (Buonanno et al. 2020; CDC 2021; Morawska 2006; Morawska and Cao 2020; Oswin et al. 2022). Aerosols (< 100 μm) generated from human expiratory activities such as breathing, speaking, singing, sneezing, or coughing can linger in the air for hours and travel 1–2 m away from the infected person who exhaled them, causing new infections over short and long distances (Wang et al. 2021). Ventilation airflows, people traffic, and convective flows can influence the movements of aerosols before being inhaled (Tang et al. 2021). Although SARS-CoV-2 virion is a nanoparticle, it is usually carried by larger particles (especially PM2.5), and can be mostly contained by masks (N95, filtering facepiece respirator, or surgical mask) (Romano-Bertrand et al. 2021). Therefore, “droplets” precaution also remains as an efficient means of protecting healthcare workers caring for COVID-19 patients (Romano-Bertrand et al. 2021).

Not limited to COVID-19 pandemics, numerous studies have evidenced that buildings are closely associated with spreading of infectious diseases. Higher risks of aerosol transmission are more likely to take place in clinic settings of older/repurposed buildings with older heating, ventilation and air conditioning (HVAC) systems (Kohanski et al. 2020). Moreover, viral infectious diseases could be transmitted across distances by aerosols, leading to large clusters of infection in short periods (Fineberg 2020; WHO 2009; Xiao et al. 2017). Therefore, resolutions for mitigating airborne transmission of SARS-CoV-2 have become imminent since exhaled viruses could accumulate with increments of staying time or number of persons, making confined spaces much more dangerous than in outdoors (Lewis 2021). In addition, aerosol transmission produced by asymptomatic individuals is also one of the major causes of SARS-CoV-2 transmission, especially in spaces with poor ventilations, longer staying duration, or large gatherings (Anderson et al. 2020).

Control measures for indoor transmission of SARS-CoV-2

Generally, the suggested precautions against indoor aerosol transmission include using natural ventilation, increasing ventilation rates, avoiding air recirculation, staying in front of the airflow, or minimizing number of people indoors (Qian and Zheng 2018). For ventilation rates, it was recommended that minimum air change per hour (ACH) standards should be 0.35 h−1 in most households, 2 − 3 h−1 in offices, 5–6 h−1 in school classrooms, 7–17 h−1 in airplane cabins, and 4–20 h−1 in different functional rooms of hospitals (ASHRAE 2020). However, large uncertainties were found in reducing indoor infection risks by only adjusting ventilation rates (Katal et al. 2021). Therefore, multiple interventions are suggested to be practiced together in measures such as adjusting room settings, numbers of total population or infected people indoors, and activity levels. Moreover, mobile air purifiers or filters in HVAC systems could be an efficient tool to save extra energy in heating/cooling systems by cleaning recirculated air accompanied with the strategy of controlling ventilation rates. It was found that the most efficient filter, known as minimum efficiency reporting value (MERV) 16, could remove > 95% particles with diameters ranging from 0.3 to 10 μm (Leung et al. 2020; Sublett et al. 2010). In addition, the portable air cleaners such as stand-alone high-efficiency particulate air (HEPA) filters that could supply effective flow rates of particle-free air can be another efficient strategy for old buildings with limited ventilation efficiencies (Shaughnessy and Sextro 2006; Waring et al. 2008).

Previous studies suggested that combinations of (i) increasing outdoor ventilation, (ii) application of high-efficiency filtration (MERV 13), and (iii) portable HEPA filters could increase ACHs from 0.32–3 h−1 to 4–6 h−1 in small-volume enclosed spaces (Allen and Marr 2020; Allen and Ibrahi 2021). Ventilators at the upper level of walls would also be more effective in air movements and ventilations (Farooq et al. 2020). Moreover, dominant flow pattern also plays a crucial role in removing contagions and cross-contamination between persons. Compared with mixing ventilation that occupants are likely to be surrounded by mixed air with uniform properties, displacement ventilations were recommended to minimize further spread of COVID-19. Displacement ventilations are capable of making occupants surrounded by newly arrived air and lifting contagions generated by infected individuals-induced towards ceiling with rising warm air (Bhagat and Linden 2020).

Preventive strategies for disease outbreaks in hospitals

There has been increasing evidence showing high potentials for viral transmissions either through air- or surface-borne SARS-CoV-2 contact in healthcare facilities (Richterman et al. 2020). It was reported that 44% of 179 cases of COVID-19 infections were acquired from hospitals (Zhou et al. 2020). The WHO also suggested that health care workers account for up to 1 in 7 cases of COVID-19 worldwide. Based on a prospective cohort study conducted in general communities of the UK and USA, higher risk for reporting positive COVID-19 test (adjusted hazard ratio of 3.40) in front-line health-care workers was found, implicating a dire situation of higher infectability of health workers even with universal masking protocols (Nguyen et al. 2020).

Primary suggestions for prevention of hospital-acquired infections were provided previously (Ducel et al. 2002). Location of outdoor air inlets is suggested to be as high and remote away from ventilation discharge outlets, incinerators, or boiler stacks as possible. In this way, clean air can move downward toward the contaminated floor to keep enclosed spaces clean with low exhausts. Also, high-efficiency filters should be essentially provided in ventilation systems of serving areas to prevent patients from potential infections or in functional rooms with clinical procedures to avoid unusual hazards such during surgical procedures. In addition, at least a velocity of 0.25 m s−1 airflow through a HEPA filter circulated into the room was suggested to reach ultra-clean air. Produced ultra-clean air could be furtherly applied in areas such as microbiology laboratories, pharmacies, special intensive care units, and operating rooms. Moreover, negative air pressure could be applied in contaminated areas or rooms for isolation of patients infected by airborne-transmitted diseases to restrict the movements of contaminated air from leaking out of the rooms (Ducel et al. 2002).

Generally, the Centers for Disease Control and Prevention (CDC) suggested that hospital-based clinic rooms require minimum ventilations of 6 ACH, operating rooms of 15 ACH, and outpatient facilities of ~ 2 ACH (CDC 2019). However, although many hospital facilities have provided adequate ventilations in a routine measure, it is highly likely that spaces where more patients are admitted or densely clustered do not have sufficient ventilation rates for infection preventions (Morawska and Milton 2020). Negative pressure ventilation alone in several functional rooms of hospitals is also not thought to be sufficient to provide protection to patients or staff (Ribaric et al. 2022).

Minimal surface-borne and non-airborne SARS-CoV-2 RNA in hospital areas utilizing HEPA filters were observed regardless room type, ventilation system, and number of ACH, indicating the importance of utilizing HEPA filters in ventilation systems (Ribaric et al. 2022). Furthermore, very low viral concentrations with significant reductions of air- and surface-borne SARS-CoV-2 were observed when ACH was above 16 h−1 (Ribaric et al. 2022). Reassessing this empirical result by using our constructed model, however, revealed no inconsistency. Namely, we confirmed that COVID-19 containment could be achieved with an ACH of 16 h−1 under certain conditions of the most stringent (bay-handwashing: tc ≤ 3 h with nc = 10) or loosest indoor setting scenario (patient bay-resuscitation: tc ≤ 1 h with nc = 120) based on basic requirements of room volumes and ventilation rates of the emergency unit in healthcare facilities.

On the other hand, it was evidenced that viable SARS-CoV-2 was isolated from air samples collected 2–4.8 m away from patients staying in a hospital room (Lednicky et al. 2020), indicating that there may be an airborne transmission with super-spreading phenomena even in a 6 ACH ward. A multivariate analysis also provided a crucial information that the odds to detect SARS-CoV-2 in rooms with negative pressure but without laminar airflow or HEPA filtration were not significantly lower than those without any mechanical ventilation, suggesting a pivotal role of effective filtration systems in ventilation facilities (Beaussier et al. 2022). Also, from a different perspective, application of additional cold air on sunny side of hospital rooms during seasonal changes is also suggested, since solar radiations-induced temperature differences were associated with contaminated air transportation from rooms to other public areas (Beaussier et al. 2022). Taken together, in addition to the existing ventilation system, adding effective HEPA filters or seasonal control of indoor airflow could be effective tools to enhance the effectiveness of ventilation systems in enclosed areas of healthcare facilities.

Limitations and implications

In this study, we adopted the Wells-Riley model to parsimoniously estimate R0 values with the most conservative exposure scenario as a baseline evaluation for R0 estimations in various functional units in two Wuhan hospitals or basic Rc considerations for the exemplified emergency unit. In our approach, we aimed to derive baseline evaluations of R0 and Rc with basic requirements of indoor settings and baseline values of physiological parameters in the condition of no intervention of control measures (e.g., masking, social-distancing) applied (Gupta et al. 2012). The reasons for choosing this scenario are to derive the baseline values of R0 with the simplest exposure scenario and to exclude the uncertainties of policy implementations such as universal masking indoors in different countries or areas. If the same indoor conditions (e.g., activity level, quantum generation number, indoor population, room volume, and ventilation) are applied, lower R0 values are expected with implementation of control measures (e.g., wearing mask), whereas higher R0 could occur if higher physiological parameters or indoor population are applied.

On the other hand, we found that parameter impacts/sensitivities on R0 are influenced by other parameter values (e.g., sensitivity of air supply rate on R0 is affected by room volume), indicating that parameter sensitivities substantially depend on exposure scenarios and indoor settings. However, the Wells-Riley model with certain assumptions and limitations (e.g., well-mixed air and uniform concentrations of aerosols) may has limitations since heterogeneous distributions of airborne SARS-CoV-2 could result in different exposure probabilities on subjects indoors.

Based on the conservative parameterizations applied in this study, higher R0 estimations are expected with the same indoor conditions when (i) more than 1 infector were in the same room or (ii) higher inhalation rates or quantum generation numbers were applied to different subjects. Notably, Buonanno et al. (2020) suggested that high quanta emission rates (> 100 quanta h−1) could be reached by an asymptomatic infectious SARS-CoV-2 subject performing vocalization during light activities, yet low quanta emission rate (< 1 quantum h−1) occurred in resting conditions. Since it would be more unlikely that vocalization performed by subjects occurs in hospitals and there is high variability in quanta emission numbers, we thus estimated this parameter ranging from 14 to 48 quanta h−1 in a relatively conservative perspective based on a previous study (Dai and Zhao 2020).

Not limited to hospitals, mitigation strategies for allowing clinics to remain operational when regional surges in cases occur are also important. Staff without patient contacts are also likely to be infected if they spend prolonged times in corridors and nurses’ stations (Azuma et al. 2020; Buising et al. 2022). Although the ability of virus transmitted from patient room into other spaces was not considered in our study, we found that exposure time is one of the most sensitive parameters for functional rooms of emergency unit. Thus, to reduce acquisition risk of respiratory viruses, portable air cleaners were suggested for medical staffs to clean the air locally and provide protections equivalent to be as much as 30 ACH (Buising et al. 2022). However, in the circumstances of building using central ventilation systems, it was found that higher air exchange rates lead to increasing concentrations of respiratory droplets at short times, longer times are on the opposite (Vlachokostas et al. 2022). Noakes and Sleigh (2009) also had consistent findings derived from the Wells-Riley equation that the number and rate of new infections between connected spaces is strongly dependent on the airflow, indicating that buildings using centralized HVAC systems may have higher probabilities in indoor transmission than buildings without using the system.

In light of the importance of protecting healthcare staff, patients, and visitors against COVID-19, our study has implications for implementation of administrative interventions including triaging procedures, limiting number of people in hospital, and cohorting patients and staffs to reduce nosocomial spread of COVID-19 (Ahmad and Osei 2021). The R0-based air supply rates could provide useful information in combination with engineering controls in parallel with effective applications of other strategies (Morawska et al. 2020).

Taken together, our analyses represent a comprehensive estimate of the minimum ACH that requires attention for COVID-19 containment to safeguard intervention policies. Moreover, changing room volumes is not much impactful on R0 than other parameters, and is also not a practical strategy for most healthcare facilities. Among these R0- or RC-associated parameters, we found inhalation rate to be highly influential in reducing the relative spread potential of COVID-19. Much higher impacts of inhalation rate were also found in smaller rooms than spacious ones, indicating the importance of controlling activity levels in healthcare facilities. We thus provide the following suggestions for preventive measures on SARS-CoV-2 transmission: (i) to prevent higher inhalation rates resulting from running, exercising, or any forms of labouring, (ii) to enhance ventilation rate to be higher than 7 h−1 if there are more than 10 people staying indoors over 1 h (yet, higher ACHs are required if more than 1 infector or higher activity level applies), and (iii) using HEPA filters to ensure appropriate dilutions of airborne SARS-CoV-2 especially in buildings with centralized HVAC system to prevent nosocomial COVID-19 infections when there is a surge of cases.

Conclusions

We offer a practical approach by using a modified Wells-Riley model to reflect the most conservative R0s in the two Wuhan hospitals and the emergency unit in healthcare buildings as a general illustration. We highlight that inhalation rates of individuals prove crucial for influencing the transmissibility of SARS-CoV-2, followed by exposure time, room volume, and air supply rate. We suggest that control measures mainly focus on the awareness of appropriately controlling activity levels, optimizing exposure time/number of people indoors, and enhancing air purifiers in an enclosed space. With the difficulties in altering room volumes of hospitals or any healthcare buildings during case surging periods, the most practical and flexible mitigation strategies would be adjustments of air supply rates or adding the HEPA systems. Critically, we also provided simulations to evaluate the success of policy actions and interventions intended to improve public safety efforts on preventing spread of COVID-19 in built environments. Our approach reconsidered from the Wells-Riley model as presented here may help provide an efficient means of impact assessment for SARS-CoV-2 transmission and assist in future interventions planning, early COVID-19 infection detection, and mitigation efforts.