An agent-based study on the airborne transmission risk of infectious disease in a fever clinic during COVID-19 pandemic.

Prevention of nosocomial infections is particularly important for the control of COVID-19 pandemic. We conducted a field study and performed extensive numerical simulations of infection transmission in a fever clinic during pandemic through an agent-based model with pedestrian dynamic and an infection transmission model. Furthermore, we evaluated the cross-infection risk of the patients influenced by the patient inject flow, medical service capability and plane layout. The service capability of fever clinic is determined by the least efficient medical session. When patient inject flow exceeded the service capability, the average dwell time, contact time, exposure dose, and risk of infection of patients all increased dramatically. With the patient inject flow exceeding the service capability, the growth rate of the contact time between patients and the cross-infection risk increased by 11.5-fold and 29.5-fold, respectively. The plane layout of the fever clinic affected the exposure dose and risk of infection. The waiting areas in the fever clinic had the highest risk, where the cumulative exposure dose of virus occupied up to 66.5% of the total. Our research will help to evaluate the biosafety of hospital buildings used for the diagnosis and treatment of infectious diseases.

Introduction

Background

Corona Virus Disease 2019 (COVID-19) has caused a huge impact on global public health security and economic development. The lives and health of people and the safety of property around the world have suffered tremendous losses [1]. Considering the damage caused by this infectious disease, researchers have been paying attention to the transmission mechanism of this disease to propose appropriate control measures.

Many studies revealed that Severe Acute Respiratory Syndrome Corona virus 2 (SARS-CoV-2) can transmit through the air, and numerous researchers have begun to focus on the transmission of viruses in indoor environments. Studies have extensively investigated the transmission routes of SARS-CoV-2 [2], which mainly transmitted through coarse droplets (>10 in diameter) from human exhalation, as well as through fine droplets (≤10 in diameter) suspended in the air for a long period of time [[3], [4], [5], [6], [7], [8], [9]]. Respiratory infection can easily spread in crowded rooms and in poorly ventilated spaces [10]. The biosafety of indoor environments in public buildings has been a cause for concern, especially in hospitals.

Due to the global outbreak and spread of the COVID-19 pandemic, hospitals around the world are faced with a large number of patients requiring screening and admission, which puts tremendous pressure on public health facilities. The ratio of potentially infectors in the crowd of visited patients in the hospitals is much higher than in other public buildings. Reports and studies showed that numerous hospitals have experienced nosocomial infections since the emergence of COVID-19 pandemic [[11], [12], [13]]. It is imperative to study the airborne transmission of the virus in hospital for reduction of the nosocomial infections.

China established a special mechanism called fever clinics to respond to respiratory outbreaks during SARS in 2003 [14,15]. In detail, a department or building in relatively separate areas of a general hospital and a high-standard community hospital across the country was set up for the specialized treatment of patients with fever or respiratory infection symptoms. This mechanism can be used to monitor influenza and infectious disease outbreaks [16], and helped China to control the pandemic caused by SARS-CoV-2 very quickly [17]. These specialized fever clinics have the role of screening patients for potential infectious diseases. However, the fever clinic also became a department with a high risk of nosocomial cross infection. Fever clinics in China, especially in Wuhan, experienced a large influx of suspected patients in the early stages of the pandemic. This greatly exceeded the services capability of these hospitals. Patients were crowded in small spaces for long periods of time, and their contact time and probability with the infected individuals in them increased significantly. To reduce the wider impact and more serious spread of nosocomial infections, the risks and patterns of virus transmission in the indoor space of fever clinics need to be studied. It is also necessary to figure out the risk of infection in relation to the layout and patients’ activities.

Many studies on the risk of airborne transmission of infectious diseases through experiments and simulations have been widely conducted. From the experimental aspect, Ai E et al. suggested that the risk of aerosol transmission could be studied with tracer gases [18]. Baboli et al. sampled the air in the ICU ward using an Anderson air sampler and found a large number of viruses within 1–3 m of the beds [19]. Chen et al. examined the positivity rate of SARS-CoV-2 at various locations in the fever clinic using Polymerase Chain Reaction (PCR) detection [20]. They found deposited and suspended viruses on the floor and in the air of the fever clinic. These experimental studies considered the mechanisms of transmission of aerosol and droplet releases from humans, but these experiments often only examined the risks associated with a single behavior of a person in a room or environment, with people set at stationary. In reality, however, it is only common for people to move complexly through the environment and cause widespread transmission. Fewer studies have been conducted on fever clinics. In the one study that could be seen so far, Zhou and Ji investigated the risk of aerosol particle inhalation by physicians and patients during consultations using experiments with dummies releasing aerosol particulate matter and CFD simulations [21]. However, the fact is that the study of infection risk in the fever clinic involves a multistep medical process and complex patients' activities.

The spread of the virus is related to specific activities of people. In several other studies on the risk of airborne transmission infection diseases, agent-based model simulations have been used to study the virus transmission. These studies simulated human activities in different life scenarios and calculated the infection risk in these activities and spaces in the event of a pandemic. Campos et al. simulated personnel activities in a temporary hospital receiving patients with infectious diseases and measured the risk of cross-infection in terms of the distribution of personnel activity density [22]. They identified the need for measures to reduce patient congregation and waiting times to reduce the risk of infection. Mohammadi et al. used a pedestrian simulation model to explore the risk of airborne transmission of infectious diseases at different social distances [23]. They studied the effect of pedestrian flow and sidewalk design patterns on the risk of infection using distance as an influencing factor for risk attenuation and concluded that appropriate increases in sidewalk size and control of social distance are necessary. Vuorinen et al. and Tsukanov et al. used an intelligent agent-based to study the risk of airborne transmission of COVID-19 virus in supermarkets [24,25]. Vuorinen et al. used the aerosol dispersion equation from the study of Asadi et al. and combined it with a pedestrian agent model to assess the risk of infection in the presence of random activities of people in public places. Tsukanov et al. introduced a stochastic probabilistic infection model related to social distance and human orientation to simulate and calculate the infection risk of customers in the supermarket under different traffic conditions and concluded that the spread rate of the virus depends on the shopping strategy of customers and the geometric space shape. Felix et al. used an agent model and CFD to study the risk of virus transmission through the air during the evacuation of a movie theater [26]. However, these studies generally assumed only that the risk of virus transmission decays with distance between people, ignoring the characteristics of airborne dispersion of droplets and aerosols containing the virus.

The focus of this study is to assess the exposure dose of inhaled airborne viruses and infection risk of patients in fever clinic. Agent-based model according to the mobility characteristic of the patients influenced by the medical process in the fever clinic integrated with the airborne virus transmission model was utilized to calculate the exposure dose of viruses. By the establishment of an agent-based simulation model of medical process, this study assessed the cross-infection with different patient inject flow in a typical fever clinic and discussed the relationship between risk variation and building layout of the fever clinic. The study will help hospital administrators develop mechanisms for operating fever clinics during a pandemic and help designers of hospital buildings understand the risk of infection in infectious disease spaces like fever clinics to design safer hospitals.

The remainder of the article is organized as follows. In section 2 we present the field study of medical process in a fever clinic. In Section 3 we present the methodology and the settings of some of these parameters, mainly including the agent-based medical process simulation model and the airborne transmission model of infectious diseases. Section 4 summarizes the results obtained from simulation and discusses the reasons for them. The last part is a summary of the conclusions of some main elements and the shortcomings of the study.

Field study of medical process in a fever clinic

We conducted a three-day field study in a fever clinic in Shenzhen, China, in January 2021. The survey duration ranged from 8:00 a.m. to 8:00 p.m. daily. During the field study, we mapped the floor plan of the fever clinic, recorded the medical process and the characteristics of 108 patients' activities in the building. The main features include the trajectory of the patients' activities, the time elapsed in each session and the speed at which they move, as well as the characteristics of avoiding obstacles. Data from the field study were collected in two main ways. One is to analyze the real-time monitor video of this fever clinic through observation and target detection programs to record patient inject flow, movement speeds, and mapped activity trajectories. At the same time, in order not to miss the view beyond the monitoring range, the researchers tracked the patients studied and recorded their trajectories and the time elapsed in each medical session on a floor plan. Fig. 1 shows the layout of this fever clinic, which consists of three main areas, i.e., clean area, potentially area and contaminated area. The height of all spaces in the building is 3 m. The specific names of rooms and area set up in this fever clinic are shown. The clean area is a dedicated corridor for medical staff and an office area for non-consultation purposes. The potentially contaminated area is a space for medical staff to put on and take off personal protective equipment. The contaminated area is the area where patients are active. Since the focus of this paper is on patient-to-patient cross transmission, the contaminated area is the area of concern.

Fig. 1

Layout of a fever clinic built according to Chinese national standards.

The medical process determines the changing location and movement characteristics of the patients within the building space. The process mainly includes some tests necessary for screening respiratory infected patients, such as blood test and nucleic acid test based on Real Time Polymerase Chain Reaction (RT-PCR) detection [27,28], chest Computer Tomography (CT) [29,30], which are essential and efficacious in the screening of patients with COVID-19 infections. Fig. 2 shows the whole process of screening patients for COVID-19 in the fever clinic. We recorded the time elapsed for patients in these sessions (see Fig. 3 ). Patients with symptoms of fever and respiratory illness were triaged to the fever clinic. Firstly, they need to take their temperature and describe their epidemiological history at the pre-examination desk and take a number through the registration machine. Then they were required to wait for their number to be called in the waiting area in the lobby and then go to the consultation room to be examined by the doctor. Patients paid for blood test and CT imaging after their initial consultation, and they waited in the lobby for their results to be printed out after completing these tests. Patients came back to the consultation room with these report forms. After completing these procedures, doctors made a preliminary diagnosis based on blood tests and CT images and arranged the patient do a nucleic acid biopsy taken. Some patients diagnosed as suspected cases will be admitted to the isolation ward of the hospital pending the results of the nucleic acid tests, and once confirmed as carriers of the virus, they were transferred to special wards for follow-up treatment. If the patients' fever symptoms were not due to an infectious disease and the results of the nucleic acid biopsy are normal, these patients were transferred to other appropriate departments for further treatment.

Fig. 2

Medical process of fever clinic and time consumption of each session.

Fig. 3

Time elapsed in each session.

The average number of patients per day during the field study was 156. The average patient inject flow was 12.5 per/h. Patients moved at a speed ranging from 0.9 to 1.5 m/s. They generally maintained a social distance of at least 0.3 m. During the statistical process we found that when the number of patients arriving per hour was less than 13 per/h, the patients mainly stayed and gathered in the Waiting Area1 and in the lobby, where they mainly waited for the results of blood tests and CT imaging. When the number of patients arriving for several hours in a row exceeded 13 per/h, Waiting Area 2 also began to fill up with patients waiting in line to be examined by the physician. This occurred mainly because it was influenced by medical processes and service capabilities. As shown in Fig. 2, the medical process in a fever clinic is linear, with a tandem relationship between medical sessions. Whether or not a queue is occurred depends on the medical session where the service is least efficient. From Figs. 2 and 3, it is clear that the session in which patients spend the most time is waiting for test results, followed by the consultation. Since the waiting time for test results was fixed without observing the sequence, the service capacity actually depended on the consultation. In the fever clinic in the field study, there were two consultation rooms, and the average service efficiency of one room was 13.3 per/h. Patients needed to complete two consultations in succession, so it can be assumed that when the patient inject flow exceeds this value, a queue will occur. These phenomena (i.e., patients crowded queues and waiting for consultation.) reflected some of the behaviors and areas that could lead to cross-infection. However, field studies did not fully account for patient activity in all arrival conditions nor did they provide data for stable working conditions, so we need to develop an agent-based model to do an in-depth study of service capacity and patient infection risk.

Simulation method

As shown in Fig. 3, this study mainly utilized the data of layout and medical process obtained from the field study in the previous section to build an agent-based simulation model to simulate patients' activities in a fever clinic. The simulation finally obtained the mobility trajectory of the patients under different conditions and combined with the infection transmission model to calculate the exposure dose and infection risk (see Fig. 4 ).

Fig. 4

Summary of the main research route.

Agent-based model (ABM) for pedestrian dynamic

The trajectory of patients in the fever clinic was simulated by an agent-based model considering the medical process. The core algorithm used to simulate pedestrian movement is the social force model, which was proposed by Helbing and Molnar [31,32]. Main content of this theory is that pedestrians will change their position, movement speed and direction according to the position, movement speed and movement direction of other obstacles in the environment. These obstacles can be other pedestrians, walls, columns, furniture, etc. Social force model expresses the change of pedestrian speed and acceleration in the form of Newton's second law, fabricates several forces that drive pedestrian movement, and in this way generates mathematical equations describing pedestrian movement:

Here is a plane vector that represents the combined force of all external forces on pedestrian at moment . denotes the attraction of the target position to the pedestrian at moment t. reflects the interaction force between pedestrian and other pedestrians adjacent at that moment. The mutual force of other obstacles w such as walls and columns at moment t for pedestrian is .

Pedestrian with self-mass travels with velocity in the desired target direction during the relaxation time (The shorter this time is, the closer the pedestrian will be to moving in the desired direction and speed.). Denoting the velocity and desired direction at moment by and , then can be expressed as

As shown in Fig. 5 (a), the direction of in Eq. (2) will always point to the destination of the pedestrian's movement, and the direction of the pedestrian's movement is determined by the combined forces of , and at moment t. When the pedestrian needs to move from the initial position to the destination, his movement speed is accelerated to the range of desired speed in relaxation time and maintained in this range until he reaches the destination (see Fig. 5(b)).

Fig. 5

Social force model: (a) schematic diagram of the terms of Eq. (1). (b) Schematic diagram of the terms of Eq. (2).

The interaction force between pedestrians follows the formula proposed by Helbing with a correction related to pedestrian sight lines:

Here the pedestrians in the model are simplified as circles, and are both simplified radii, and is the distance calculated from the respective center points of pedestrians and at moment . represents the unit vector at that moment, whose direction is always from pedestrian to . The parameters, i.e., A, B, C are mainly used to calibrate the strength of the forces acting between pedestrians as well as the range and distance maintained. Their values are mainly influenced by specific activity scenarios. In this study, these values are mainly verified and calibrated by the activity patterns of patients in hospital reality, shown in Table 1 . and are two functions used to correct the optimization. is a function that considers the anisotropy of pedestrian viewpoint effects, referenced from Marlow et al. [33]. is a function that counteracts the repulsive force of body compression during pedestrian contact, and it only equal to zero if the pedestrians are touched.

Table 1

Social force model calibration parameters.

Parameter reference	Parameters	Value
Mass of a pedestrian	m_i	59–69 kg
Desired speed	vi0	0.9–1.5 m/s
Relaxation time	τ_i	0.4–0.6 s
Diameter of a person	r_i	0.375 m
Social force parameter A	A	2000 N
Social force parameter B	B	0.3 m
Social force parameter C	C	120000 N/m

The interaction force between pedestrian and other obstacles, e.g., walls, columns, etc. can be written asWhere is the distance between pedestrian and other obstacles at time . represents the unit vector at that moment, whose direction is always from pedestrian to obstacles.

Agent-based model parameters and validation

The establishment of an agent-based model of the medical process of fever clinic required three main parts. Firstly, the establishment of a 3D model of the patients' activities space corresponding to Fig. 1; Secondly, the setting of parameters related to the patients’ activities characteristics based on the results of field research; Finally, the construction of the route and logic of the patients' visits based on the medical process and the time elapsed in each session.

As for the number of people moving around in the fever clinic which highly effects the exposure dose of viruses and infection risk, we controlled this parameter by setting the number of patients entering the fever clinic per hour (i.e., patient inject flow ). The values of in this study range from 3 to 25 per/h. In addition, the parameters in the social force model describing patients' movements were set according to the field study, shown in Table .1. Where the human body mass and size mainly refer to the range of values in Human Dimensions of Chinese Adults (GB/T 10000-1988). The values of desired speed and relaxation time were determined by the range of the patients' moving speed and the time elapsed for them to accelerate from zero to a certain moving speed in the field study. Social force model parameters A, B and C that determine the effect of destinations and obstacles on pedestrians were mainly refer to the empirical values in Helbin and related studies [31,32], and we determined their values by referring to these empirical values combined with the degree of agreement between the field study and the simulation results (see Fig. 6 ). The other main step was to establish the logic and routes of patients’ movements in the fever clinic based on the medical process in Fig. 2. This process also involved setting the amount of time the patients need to spend in each medical service session. These time-related data were mainly referenced to the field research (See Fig. 3).

Fig. 6

Validation of the accuracy of agent-based models: (a) Trajectory of 108 pedestrians in simulation models and field study measurement; And (b) actual and simulated dwell time data of various medical sessions.

The agent-based model was validated by comparing simulation results with on-site measurement. We simulated the patient inject flow of 12 per/h and obtained trajectory and time data for 108 patients at the time of their visit. In terms of time elapsed, as shown in Fig. 6, cumulative probability distribution of the simulated results of medical sessions (i.e., Pre-examination, register and take number, blood test, chest CT examination, Consultations, Nuclei acid test) time elapsed are highly consistent with measurement in field study.

As shown in Fig. 6, the trajectories of patients' movements obtained from the simulation are similar to those recorded from the field study. In contrast to the simulated trajectories, the real patient trajectories are also distributed in a small number of locations that were not reached in the simulation, but this is mainly due to a small number of heterogeneous behaviors of patients that are not related to the medical process (see Fig. 2). It should be noted that in the simulation based on the agent-based model, the characteristics of the patients' movements were defined as being similar or identical. Such a homogeneous description is idealized because there are differences in human activities. However, the probability of individual patients' non-treatment related behaviors occurring is small and unpredictable compared to the whole medical process. We therefore ignored these activities in patients' behavior, such as random activities like going to the toilet and small, because these behaviors are not included in the medical process and cannot be counted as probable.

Infection transmission model

According to the various sizes of fine and coarse droplets expelled by the infector, four transmission routes of respiratory infection were considered in this study. As shown in Fig. 7 (a), exposure of fine droplets with a final diameter below 10 by the short-range airborne route () and the long-range airborne route (), direct inhalation () of coarse droplets with a diameter ranging from 10 to 100 and direct deposition () on the facial mucous membranes of the coarse droplets (i.e., eye, mouth, nose). The distance between the infector and the susceptible and the face orientation were taken into consideration in this study. The location and face orientation of the individuals are depicted in Fig. 7(b).

Fig. 7

Scheme of transmission routes of infectious diseases: (a) Multi-routes of transmission; and (b) spatial position between the infector and the susceptible.

Exposure dose of fine droplets by short-range airborne route

Taking the face orientation into consideration, if the position of the susceptible person is not in the spreading area of the cough jet from the infector, the exposure dose from short-range airborne route is simplified to be zero. The virus concentration in the jet flow will be diluted with the air entrainment along the streamwise direction. Thus, the exposure dose of fine droplets by short range airborne can be calculated using Eq. (5).Where is the pulmonary ventilation rate, and its value is 0.48 m3/h [34]. We considered the effect of coughing and assumed that cough can generate a respiratory jet cone with a spreading angle of α. Here α = 5/36. is function used to determine whether a susceptible person is within the cone angle of the cough jet zone (see Eq. (6)). The angle between the orientation of the susceptible and infected individuals and their connecting lines are denoted as and , respectively. We assumed that the orientations of the patients' bodies were the same as the directions of their own movements, and that the head was always aligned with the orientation of the body without rotation. These moments of and will be used to determine whether a susceptible person is within the range and attenuation effect of short-range transmission of an infected person, and the exposure dose and risk of infection is actually the sum of the integral of the exposure to the short-range transmission route of a susceptible person and the exposure to the long-range transmission. is the dilution intensity factor, as shown in Eq. (7), which is mainly related to the distance.

Here is the diameter of the mouth during coughing, and its value was set to 0.02 m is the distance between the infected and susceptible person.

Exposure dose of fine droplets by long range airborne route

Spraying droplets with a final diameter below 10 could evaporate quickly and suspend in the air for a long duration. Concentration variation in enclosed space with a well-mixed space assumption could be expressed as:Where is the volume of the enclosed space, is the indoor virus concentration attached to droplet nuclei with a diameter of , is the virus concentration expelled by infection, is the expiration rate, and is the decay rate of the indoor virus concentration.

Here is the air change rate and set as 6 h−1, referring to Chinese standard (GB50849-2014). (h−1) represents the rate of virus removal due to filter filtration when air is circulated through the air conditioning system [35,36]. indicates the virus elimination rate due to deposition (h−1), and it is mainly determined by the area and deposition velocity with respect to the upward-facing, downward-facing and vertical surfaces in the space [37]. is the viral removal rate resulting from viral death due to biological decay (h−1), which is mainly influenced by environmental conditions, here  = 0.63 h−1 [38].

Exposure dose of fine droplet nuclei by long range airborne route can be calculated using Eq. (10).

Direct inhalation of coarse droplets

For the coarse droplets with a final diameter ranging from 10 to 100 , the spraying droplets will deposit and depart from the jet flow due to the gravitation. is the probability of droplets with an initial size of to reach a distance of before falling out of the respiratory jet at an initial speed of . is affected by the mouth opening size, initial velocity of the jet, and the room temperature and humidity, which was modelled by combing the buoyant round jet model and droplet evaporation and motion models by Wei and Li [39]. The dose due to direct inhalation of medium droplets can calculate with Eq. (11).

Direct deposition of medium droplets on the facial membranes

The face orientation of the susceptible is taken into consideration in this study. So, the dose due to direct deposition in the facial membranes can calculate with Eq. (12).

Here is a parameter considering whether susceptible patients’ head in the cough jet zone. The possibility of considering inhalation is zero when two people are facing each other backwards. is the area of the site where a susceptible person may enter the pathogen, containing mainly the oral and ocular mucosa, and its value is 10−3 m2.

Infection risk calculation by Monte-Carlo simulation

We calculated the infection risk for patients () 2 using Eq. (13).where k a parameter related to the dose that can cause infection, for coronavirus the infectious dose was from 10 to 100 RNA copies [40]. Since we found no pathogen reference values in the known literature that correlate with the infectivity k of SARS-CoV-2, given the similarity between SARS-CoV and SARS-CoV-2 we refer to the values in the study by Watanabe et al., here k was taken as 55 RNA copies. Specifically, the viral load in these spraying droplets with different diameters were variable, the fine droplets with a diameter less than 10 μm have a viral load of 2.08 × 106 RNA copies/ml. The coarse droplets with a diameter lager than 10 μm have a viral load of 5.47 × 103 RNA copies/ml [41]. Aerosol particles of different particle sizes are deposited in the human respiratory tract at different sites, so the dose of infection from different routes may vary [42]. Since there is a lack of studies and data on the infectious dose at different sites of the respiratory tract, only one challenger experiment in London, UK, has studied the total dose that may cause infection [43]. Here we simplified the dose of infection from different exposure routes and used the same infectious dose. However, we have also taken into account the different viral loads for aerosol particles of different particle sizes to bring the calculated results closer to the real values.

To study the effect of entering a different number of initially infected individuals on the infection risk of other patients and the exposure dose, we introduced the proportion of initial infections to the total number of patients for five scenarios, i.e., 1%, 3%, 5%, 7% and 9%. In reality, the initial number of infected patients cannot be determined in advance. We obtained a non-dimensional parameter for the probability of infection by using Eq. (14). can be defined as the expected number of secondary infected patients generated by an initial infectious patient over a period in the fever clinic. It can be used as an important indicator in the assessment of prevention and control of cross-infection between patients in the hospital.

In Monte-Carlo simulation we randomized the initial infected individuals among all patients of the susceptible occupants and then calculated the exposure dose for 9 h in the fever clinic. The number of Monte-Carlo simulation runs was set as 800. The final values of exposure dose and infection probability under different proportions of initial infected persons were averaged from the 800 runs.

Patients entered the fever clinic sequentially according to the patient inject flow . Patients were constantly entering and leaving the fever clinic under the same medical process. Patients receiving different medical services were distributed in different spaces and locations during the simulation. There was a temporal dislocation in the patients' visits, so the agent-based model recorded time-stamped information for each patient, including when they entered and left and locations at each moment. The Monte Carlo simulation program was used to randomly determine who were the infectors according to proportion of the initial infectors. Then, the program could judge whether the susceptible person was in the same place at the same moment with the infectors based on their timestamp and corresponding coordinates. The infected and susceptible persons will only be considered in the exposure dose calculation when they are in the fever clinic room at the same time.

There are different areas and rooms in the fever clinic (see Fig. 1), and the aerosols released by the patients will well-mixed in each room. but there will be concentration differences between rooms, so the calculation program identified the room and area where the infected and susceptible persons were located before begun the calculation, a susceptible person will only be exposed to aerosols in concentrations that are present in his area or room. When an infected person moves into a room, he only affects the aerosol concentration in that room and the susceptible person is only exposed to the concentration in that room. In terms of short-range transmission, simulations and calculations were mainly performed based on the dispersion characteristics of exhaled droplets and aerosols, and then the short-range exposure was calculated based on factors such as distance between individuals and facial orientation. In the short-range transmission model, we mainly considered the inhomogeneous distribution characteristics of aerosols in indoor air. In the long-range transmission model, this paper adopted the lumped parameter method, and we assumed that this part of the propagation can quickly reach a well-mixed state in independent spaces and regions, but also considered the effects of gravitational deposition, air conditioning filtration and virus deactivation.

Results and discussion

Dwell time and service capability

We used the agent-based model to map the patients' location and trajectory (see Fig. 8 ). What can be found is that as r increases, especially above 13, more patients gathered in the fever clinic at the moment of the end of the simulation because the service capability reached the upper limit, and the waiting areas in the lobby and corridors were the places where the number of gathered patients was higher and where more contact behaviors occurred. As shown in Fig. 9 (a), the fever clinic is limited in the number of patients who can complete all tests in 9 h. This value is about 98 people, and it peaks after  = 13 per/h, which represents the service capability of this fever clinic. This is mainly because the medical processes in the fever clinic are tandem with each other, so this upper limit is related to the least efficient one of all medical sessions. Among them, the medical session of waiting for test results needs to be excluded because time elapsed on it for patient does not increase as more patients need to wait in queues. In this study, doctor in each consultation room took an average of 4.5 min to complete a patient's inquiry (see Figs. 2 and 3), which means that he was able to complete approximately 13 visitors. This is the reason why the number of patients able to complete all exams reaches a peak at  = 13 per/h. When is greater than 13 per/h even if more patients enter the fever clinic per hour no more tests can be completed. So, we define this key value as the reasonable patients inject flow. The average dwell time, contact time, exposure dose, and risk of infection can all increase significantly as exceeds this reasonable value (see Fig. 9，Fig. 10 and Fig. 11 ).

Fig. 8

Positions, orientations, or directions of the moving of the patients (t = 9 h) with a patient inject flow of 13 per/h (a), 15 per/h (b) and 20 per/h (c). The arrows represent the direction at which the patient was facing or moving.

Fig. 9

Variation of the number of treated patients and the time index with the patient inject flow: (a) Number of patients with completed and incomplete consultations at t = 9h; And (b) average dwell time of patients and average contact time of others.

Fig. 10

Timestamped information of patients entered and left the fever clinic: (a) R = 9 per/h. (b) R = 13 per/h. (c) R = 17 per/h.

Fig. 11

Exposure dose and infection risk with different patient inject flows: (a) Proportion of various exposure routes; (b) Average exposure dose per capita with different proportions of initial infection; (c) The risk of infection with different proportions of initial infection; And (d) the expected number of secondary infected patients generated by an initial infectious patient in the fever clinic (ε).

The duration of stay and contact can be calculated based on the data of their trajectory changes. The average dwell time is the average elapsed time by all patients from the time they entered the fever clinic to the time they left when they completed all examination sessions or the end of simulation (see Fig. 9(b)). The average dwell time increased slightly when patients inject flow <13 per/h. Within this range patients required to wait in line for shorter periods of time or even without waiting. The average dwell time was approximately 0.86 h, close to sum of time elapsed of all medical examination sessions and the time needed to walk (0.83h). When >13 per/h, the average dwell time became progressively larger. Fig. 10 shows the timestamp information for each patient entered and left the fever clinic within 9 h for different patient inject flow . This also shows the time spans of the patients in the fever clinic. It is clear that when the value of is less than 13 per/h, the order in which patients arrived does not have a large impact on the time elapsed on their visits. The time spans of patients that entered and left the fever clinic are highly variable in different patient inject flow . When  = 13 per/h, patients started to need to queue in some medical sessions, and the time elapsed in the visit increased but with little variation between patients. When >13 per/h, the time elapsed for patient visits increases with their arrival order and the range of time spans that overlap between them also increases, which means that more patients were present in the same space and in contact at the same time. As shown in Figs. 8 and 9(b) and 11, queuing behavior occurred because the number of patients visiting during the same time period exceeded the medical service capability (The maximum number of diagnoses a physician could complete in 1 h).

A long duration of close contact can result in a large exposure dose and a high infection risk. When the distance between patients were less than 1 m were deemed to be the onset of contact, we counted the average contact time of this contact behavior between patients in the fever clinic (see Fig. 9(b)). The contact time with  = 13 per/h as the cut-off shows two linear growth relationships with different slopes, the slope is 0.0239 when <13 per/h and 0.2738 when >13 per/h. The growth rate of contact time between patients increased by 11.5-fold when over this critical value than below.

Exposure dose and infection risk

Fig. 11(a) shows the proportion of the patients’ exposed viral dose by various transmission routes to the total exposure dose. The exposure dose came mainly from long-range route aerosol and short-range route aerosol transmission . The proportion of exposure dose by fine droplets with a diameter below 10 was up to 90%. The exposure dose through droplet inhalation and droplet deposition was always a relatively small percentage. The proportions of these two routes fluctuates only slightly at <13 per/h, and beyond this value the proportion of gradually becomes larger while the proportion of becomes smaller, and eventually the values of both are close. This is because behaviors such as queuing and waiting for consultation became progressively more frequent as increased, especially when exceeded 13 per/h, Waiting Areas and corridors were crowded with waiting patients (see Fig. 9). The fever clinic completed all tests for a maximum of about 98 patients in 9 h (see Fig. 8(b)), and the increased of patients in the room after exceeding the upper limit made them more likely to be in close contact or even unable to guarantee a safe social distance (see Fig. 9), which made the value of increase rapidly and the chances of droplet transmission become more.

As with the general perception, Fig. 11(b)(c) shows that more initially infected individuals entered the room put other patients at a higher exposed dose and infection risk. The exposure dose increase with under the same conditions of different initial infection proportions (). When <13 per/h, the average exposure dose and the risk of infection increased slowly. When >13 per/h, the average exposure dose and risk of infection increased substantially. The rate of increase in infection risk before and after  = 13 per/h differed nearly 20-fold when initial infector proportion  = 9%. As shown in Fig. 10, when ≤13 per/h, there is little difference in the time elapsed on visits between patients, and there were fewer contacts and waiting behaviors. When >13, the number of patients increases, and the time elapsed by patients on visits increases substantially with the occurrence of waiting behavior and the arrival sequence. And there was an increase in the range of time spans of overlap between patients in the fever clinic. So that the exposure time, exposure dose and risk of infection of patients in the same time period increase substantially as a result in the Monte-Carlo simulation calculation.

As shown in Fig. 11(d), the curves of represent the expected number of secondary infectious patients that may be generated by an initial infectious patient over a period. is a dimensionless indicator, i.e., its magnitude is not related to the unit. What can be found is that the curves of under different initial infector proportion conditions consistent. The value of is the same under the same patient inject flow. This means that this dimensionless parameter is not influenced by the initial proportion of infectors . Thus, it can reflect the inherent pattern of risk variation due to patient inject flow , medical process and fever clinic floor plan. with  = 13 per/h as the cut-off shows two linear growth relationships with different slopes, the slope is 0.0005 when <13 per/h and 0.0146 when >13 per/h. The growth rate of increased by 29.5-fold when patient inject flow over the service capability than below.

Impact of plane layout

To study the effect of layout on the risk of infection, we calculated spatial distribution of the cumulative time of occurrence of close contact behaviours and the cumulative exposure dose on the layout (see Fig. 12 ). Since each room served only one patient at a time, the cumulative exposure dose and contact time for these rooms were not displayed. The increase of exposure doses and contact behaviours occurred mainly in public areas accessible to patients other than rooms. As shown in Fig. 13 , to further understand the relationship between the different blocks in terms of quantity we divided the layout into 8 blocks and calculated the total cumulative contact time and exposure dose separately (see Fig. 13(b) and (c)).

Fig. 12

Spatial distribution of important index: (a) Cumulative contact time in each space of the fever clinic at patient inject flow (R = 13,15 and 20 per/h); And (b) cumulative exposure dose in each space of the fever clinic at different patient inject flow (R = 13, 15 and 20 per/h) with an initial infection proportion of 5%.

Fig. 13

The relationship between intensity and spatial location: (a) Patients' activity area division; (b) Cumulative contact time of different areas; And (c) cumulative exposure dose of different areas (with an initial infection proportion of 5%).

The cumulative contact time and exposure dose of different blocks show different increasing trends and characteristics with the patient inject flow. When <13 per/h, the cumulative contact time and exposure dose growth was significant for block A1 only. This was because waiting for examination results in the waiting area under such patient inject flow was the main condition to cause close contact. When exceeded 13 per/h, the cumulative exposure dose and contact time all increased sharply. The significant increases first occurred in blocks A1 and A6. Other blocks are A2, A4, A5, A8, A3 and A7 in descending order of cumulative contact time and cumulative exposure dose increase rate. This was because as the increased, the number of patients who had to queue and wait for test results also became larger, and the number of patients at Waiting Areas in the lobby and corridor became overcrowded. As shown in Fig. 13, the cumulative exposure dose share of these two blocks was highest at  = 12 per/h, i.e., 66.5%. Also, because of the central location of A6, patients frequently walked through this area and were in close contact with patients in their seats and other patients passing by.

As a result, the waiting areas and their surrounding corridor would be the areas with the highest risk of infection in that fever clinic. For the layout of fever clinic, this layout of the fever clinic with the corridor in the middle is not conducive to improving the biosafety of the space. Because this approach saves floor space and facilitates patient pathfinding but also means that the corridor has a higher utilization rate. Patients need to travel to and from rooms through the corridor, which greatly increases the number and duration of close patient encounters. Designers should consider allowing patients to walk in one direction to reduce the chance of close contact between infected patients and others and should also avoid locating waiting areas near spaces where patients frequently pass and stay.

Limitations

In this work, we neglected the effect of airflow organization in the modeling of infectious disease transmission. The CFD technology simulating the airflow organization in the fever clinic can be considered in subsequent studies. With respect to exposure dose and infection risk, the dose reference values for SARS-CoV-2 to reach pathogenicity are not known. The fact is that various virus variants have great differences and we compared only the relative risks. In this study this value we referred to the value of SARS-CoV, but this did not prevent us from studying the relationship between exposure dose, infection risk and patient inject flow and layout in a fever clinic. The location of deposition of virus-containing aerosol particles in the human respiratory tract from different exposure routes varies, and therefore the dose of infection caused may be variable. However, due to the lack of research evidence on the infectious dose of SARS-CoV-2, we have simplified the calculation of the risk of infection by using the same infectious dose. The Agent-based model developed in this paper was based on activity data from only 108 patients in the field study. More data needs to be collected to validate the model and calibrate the parameters using more accurate pedestrian localization techniques, such as those obtained through more accurate target detection algorithms or the Ultra Wide Band localization techniques (UWB).

In addition, this paper only studied and analyzed the operation of fever clinics during the early stages of new infectious diseases, ignoring some protective measures that may be implemented later in some hospitals, such as the requirement of a large social distance between people and the wearing of masks. We estimated the exposure dose of the virus conservatively, and the values were larger compared to the period when protective measures were taken, but such estimates are useful for engineering applications and medical management. We will analyze the role and impact of fever clinics of different building sizes and layout types, as well as different protective measures, in future study.

Conclusions

The risk of infection transmission in specialized infectious disease screening medical facilities was studied by numerical simulation. We performed a verified agent-based model to simulate the patient trajectory in a fever clinic according to the medical process. An infection transmission model associated with coughing behavior consisting of four transmission routes, i.e., exposure dose of fine droplets by long-range airborne route, exposure dose of fine droplets by short-range route, direct inhalation of coarse droplets and direct deposition of coarse droplets on the facial membranes, was utilized to calculate the exposure dose and risk of infection. We also proposed a dimensionless indicator representing the expected number of secondary infections generated by an initial infectious patient to assess the risk of infection in fever clinic buildings and investigated the impact of building layout and the patient inject flow. Our study leads to several main conclusions.

The maximum number of patients that can be treated in a fever clinic per hour depends on the least efficient medical session. The threshold of the patient inject flow, i.e., the critical service capability, was determined by the consulting time by doctors in the surveyed fever clinic. Above this threshold, both the exposure dose and risk of infection increase dramatically, and the growth rate of contact time between patients increased by 11.5-fold.

Exposure of the virus-laded fine droplets with a diameter below 10 μm occupied over 90% of the total exposure dose among the four transmission routes. As the patient inject flow increases, the exposure dose from the long-range route decreases while the exposure dose from the short-range route increases.

The expected number of secondary infections generated by an initial infector was independent of the initial proportion of infectors in fever clinics. It is influenced only by the patient inject flow, medical process, and layout. With the patient inject flow exceeding the critical service capability, the growth rate of the cross-infection risk increased by 29.5-fold.

Layout of the fever clinic can affect the cumulative contact duration, exposure dose, and infection risk. The cumulative exposure dose in the waiting areas accounted for up to 66.5% of the total. Placing waiting areas in locations where patients pass frequently poses a greater risk of infection.

Our research will help to evaluate the biosafety of the fever clinic and help architects and hospital managers put forward specific designs and management strategies to reduce the risk of cross-infection.

CRediT authorship contribution statement

Junjie Wang: Writing – original draft, Visualization, Conceptualization, Data curation, Methodology, Software, Validation. Haida Tang: Writing – review & editing, Methodology, Conceptualization. Jingwei Wang: Formal analysis, Software. Zhitao Zhong: Software, 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.