








key: cord-354254-89vjfkfd
authors: Peng, Shanbi; Chen, Qikun; Liu, Enbin
title: The role of computational fluid dynamics tools on investigation of pathogen transmission: Prevention and control
date: 2020-08-31
journal: Sci Total Environ
DOI: 10.1016/j.scitotenv.2020.142090
sha: 
doc_id: 354254
cord_uid: 89vjfkfd

Transmission mechanics of infectious pathogen in various environments are of great complexity and has always been attracting many researchers' attention. As a cost-effective and powerful method, Computational Fluid Dynamics (CFD) plays an important role in numerically solving environmental fluid mechanics. Besides, with the development of computer science, an increasing number of researchers start to analyze pathogen transmission by using CFD methods. Inspired by the impact of COVID-19, this review summarizes research works of pathogen transmission based on CFD methods with different models and algorithms. Defining the pathogen as the particle or gaseous in CFD simulation is a common method and epidemic models are used in some investigations to rise the authenticity of calculation. Although it is not so difficult to describe the physical characteristics of pathogens, how to describe the biological characteristics of it is still a big challenge in the CFD simulation. A series of investigations which analyzed pathogen transmission in different environments (hospital, teaching building, etc) demonstrated the effect of airflow on pathogen transmission and emphasized the importance of reasonable ventilation. Finally, this review presented three advanced methods: LBM method, Porous Media method, and Web-based forecasting method. Although CFD methods mentioned in this review may not alleviate the current pandemic situation, it helps researchers realize the transmission mechanisms of pathogens like viruses and bacteria and provides guidelines for reducing infection risk in epidemic or pandemic situations.

volume, contact angle and environmental temperature were analyzed and the lifetime of droplets under those conditions was investigated. The evaporation of droplets will also be affected by the dust in the air, and this factor should be also considered in the future.

Different from other particles, pathogens are much smaller and their diameters are generally no more than 100nm and their motion is largely affected by flowing air, hence it is difficult to analyze their trajectories directly in the atmospheric environment. With the development of computer science, a new method based on Computation Fluid Dynamics (CFD) can be used to solve this problem and it has been already well developed over the years. [20] and in the next decades, an increasing number of investigations about air pollution, atmosphere environment and pathogen transmission can be found.

As mentioned above, the droplet can bring the pathogen into the airflow and hence cause infectious diseases due to the spread of it. Normally the droplet with pathogens is generated by coughing or sneezing from the infected and the procedure of droplets generated by sneezing is shown in Fig.2 : The impact of COVID-19 is global and the pandemic situation is closely related to the health of every individual. It does not mean that there is no way to prevent or control it effective vaccines are unavailable though. Understanding the transmission of infections such as COVID-19 in various media is of great importance. In this review, the principles of different CFD algorithms are described concisely and intuitively; Theories and applications of CFD in investigations of pathogen transmission are summarized. The objective of this research work is to indicate the important role of CFD method in analyzing pathogen transmission. Through summarizing various applications of CFD method, the transmission mechanism of pathogens and prevention methods are also concluded in this work.

Three steps are necessary for numerical analysis by using CFD tools:

(1) Generating the mesh model with high quality is the key to ensure the accuracy of calculation;

(2) Boundary conditions are required to define variables at the boundary.

(3) Different algorithms that can be selected in CFD determine the way of iteration.

This work carried out in this section is to summarize the feature of CFD from three aspects: simplification, algorithms diversity and maneuverability.

Different from experimental methods, the CFD method based on mathematical models that can be operated on computers is effective and cost-saving. In numerical simulations, the pathogens are carried by small particles like solid particles or droplets can be defined by calculation models. Although the biological properties of the pathogen are complicated and various, the shape feature of the pathogen carrier is relatively simple to describe. In CFD, those particles can be defined as spheres, tetrahedrons, hexahedrons and even by the shape factor, then the pathogen transmission in different environmental fluids can be solved by utilizing multiphase models. Moreover, the transport species model can be also applied to simulations of it. In this model, the infectious pathogen in the air is defined as the pollutant source with a constant concentration (generally measured by the field experiment). Characteristics of 

Fourier heat transfer law used to describe the heat exchange:

Fick law used to describe the mass exchange: (J 1j is the source diffusion relative to coordinates, D 12 is the diffusion coefficient between two sources) 1 1 1 1 12 12 12 ()

Reynolds transportation law calculates the source quantity in control volume at time "t", which can be described as:

Introducing the continuous equation:

And Guass law (divergence law)

Then, the improved transportation can be written as:

Combining the balance equation of forces:

Then, the equation can be written as the form shown below:

Considering the acceleration caused by forces except the drag force and solving the particle motion in each step by iterative calculation:

Besides, the Volume of Fluent (VOF) model performs well in simulating pathogen transmission, especially in the gas-liquid interface. In a control volume, the total value of each phase equals 100%

and there are three situations in VOF:

If the volume fraction of "q" phase is  ,then:

(1) 0 α  , no "q" phase in this cell;

(2) 1 α  , the cell is full of "q" phase;

(3) 0< α <1, interface between "q" phase and other phases can be found in the cell.

The momentum equation and the energy equation of VOF are determined and shared by each phase.

The momentum equation mainly depends on characteristics and volume fraction of each phase and it can be written as below:

Energy equation of VOF can be written as:

J o u r n a l P r e -p r o o f

K eff is Effective Thermal Conductivity; J j,q is diffusion flux of "J" phase in "q" phase while the h j,q represents the enthalpy of it; S h is the volume of the heating source defined by users. The energy was defined as a variable relating to the average quality in VOF: (17) Resistance characteristics in all directions are assumed the same, and the equation can be written as:

Generally, the inertia resistance coefficient C 2 and viscous coefficient   are needed as the parameter of the boundary condition. Taking the medical mask as an example and the way of obtaining these parameters are shown in Fig.3 :

The pressure difference (P 1 -P 2 ) between both ends of material from the mask as shown in Fig. 3 J o u r n a l P r e -p r o o f can be measured under a velocity input (V i ). The relationship between pressure difference and the input velocity can be described by the equation as:

Then the coefficient C 2 and   can be calculated in the case of density  and thickness n  are known.

Some of investigations about transport species model and multiphase model are listed in Tab Several algorithms are mainly used in recent as summarized in Table. 3. Although the mechanism of pathogen transmission in the fluid is complex, the motion of pathogens still follows the hydrodynamics law and can be solved by mathematics models of CFD algorithms. For example, the LBM method can be used to solve pathogen transmission in small-scale while FDM method can be applied on the large-scale transmission of the pathogen.

CFD tools are in high compatibility and their computing files can be transferred in a variety of software. In general, the structure of CFD software consists of three parts: pre-processing, solver and post-processing and Fig. 4 below shows some options of each part. 

Pathogen transmission in the environment is a complex process. For the sake of the accurate simulation result, the calculation model and parameters of the simulation are necessary. Furthermore, epidemic models should be taken into account in numerical simulations. By using experimental methods to get the data that is required in the boundary condition is important, besides, experimental data are also needed to validate the simulation result. This section summarizes various epidemic models that should be used in the simulation. Moreover, experimental methods which can be applied to analyzing pathogen transmission are presented in this section as well. Although some of the experiments summarized were not used in combination with CFD methods, they can provide valuable references for similar studies by using numerical simulations.

Poussou, et.al [44] investigated the effects of moving people on pollutant diffusion and airflow.

By combining the PIV experiment technology, they used CFD method with a second-order upwind scheme to simulate the airflow. The Re-Normalization Group (RNG) k-ε was used in simulation in order to solve the turbulence with the good performance of accuracy, efficiency and robustness; In Gao and Niu [45] study, RNG k-ε model including the effect of low-Reynolds-number is used to solve the airflow and the diffusion of tracer gas which can represent the contaminant transmission are calculated by the equation below:

Where t,  and  are time, air density and tracer gas concentration respectively.

Unsteady flow is a big challenge in accurate simulation as Zhang, et.al [46] indicated. Flow in the environmental channel is always unsteady, and it hence increases the complexity of simulation on pathogen transmissions. How to treat an unsteady flow as the steady flow in practice is still a difficulty.

By defining the wave in hydraulic calculation can effectively simplify the disturbance in unsteady flow.

Capillary wave [47] can reflect the disturbance brought by some factors to surface of fluid which can be written as:

(1) For shallow waves:

(2) For deep waves:

Ku [48] presented a "waveform" method to model unsteady flow in blood which reflects the relationship between time and volumetric flow rate: Fig.5 Volumetric flow rate Mantha, et.al [49] used this method in the simulation of biological flows and found the relationship between wall shear stress and the location of the aneurysm; Nanduri, et.al [50] also used "waveform" to solve the unsteady laminar flow and the objective of this study is to build a human body surface model to simulate the airflow around the body. Although this method is useful for analyzing particle transportation in biological flows, it is not suitable for simulating unsteady flow in the atmosphere due to greater disturbance.

More, in order to simplify the model for analyzing the airflow in building, Axley [51] presented a Multi-zone model which allows users to calculate the hourly rate of airflow between various rooms and Dols and Walton et.al [52] improved this model by providing the equation of mass conversion as:

Based on the dispersal theory which is not limited to the wall-mixed region, Multi-zone model parameters should also be considered as well.

Airflow caused by temperature difference will affect pathogen transmission. Chen, et.al [56] simulated the three cases by combing the Multi-zone model and two-way air flow effect in order to demonstrate the effect of temperature difference on air quality of indoor. It can be found from one of the cases they studied, the airflow generated by the temperature difference between bathroom and corridor can transport infectious pathogens, and hence the door of infected zoom should be closed as they suggested.

Closing doors and windows in a room is not equivalent to obtaining a closed space. The crack of the door and windows is always ignored by researchers when simulating the airflow or pathogen spreading in the building or a single room. By using Multi-zone method in CFD simulation, Yang, et.al [57] analyzed the effect of stack and wind effect on contaminating dispersion and found that these factors will cause the contamination horizontally or vertically spread. Their research also indicated that the pollutant gas can be transported through cracks of doors and windows and may cause infectious disease.

Because of the great effectiveness, Multi-zone method was widely used in many cases which can be found in Wu (1 )

Where S is the susceptible people in an area, I is the number of infectious people and p represents the pulmonary ventilation rate of susceptible people.

Zhu, et.al [64] investigated the potential risk of infection in public transportation by using Wells-Riley model in CFD simulations. It was proved in their study that the closer to the operating exhaust in the bus the infected person is, the smaller the infection risk bringing to others is. Besides, this study indicated that the ventilation system of most of buses is not effective because there is only one single exhaust was located in the middle of the cabin or the back wall. Yan, et.al [65] studied the transmission of coughing particles in the breathing zone of people. In their investigation, the method that combines the Wells-Riley model and the Lagrange model in CFD was used. It was illustrated from this study that the location of releasing particles will affect the particle travel distance. Based on the Well-Riley model, this research work has also presented a quantifiable approach to assess the infection risk of passengers. These studies are helpful for improving the design of the vehicle ventilation system and hence reduce the infection risk though, they did not consider the effect of altitude on airflow patterns in vehicles.

The Wells-Riley model can also be applied to building simulation. Niu Based on physical characteristics like aerodynamics of respiration droplets, Chaudhuri, et.al [82] Proposed a numerical model for the early state of Covid-19 pandemic by integrated the chemical mechanism and pandemic evolution equations. The " " this work derived by using the theory of collision rate represents the lifetime of the droplet. It can be written as: Some investigations based on these models are listed below in Tab.5:

More, Hathway [92] combined the CFD method and SIR model in order to analyze pathogen transmission in hospital space and Asanuma and Kazuhide Ito [93] predicted the exposure risk of the population in the hospital by using CFD with considering the SIR model. From these investigations, it can be found that this epidemic model is well performed in simulating the spread of infectious diseases.

However, the number of researches that applied these models to CFD simulation is still a small amount due to the complexity of modelling and calculation in simulating the airflow or particle transport among a crowd of people.

In CFD simulation, not only the mesh model is crucial but also the parameter of simulation is of great importance to let users obtain the results they require. Generally, the boundary condition such as velocity, pressure, turbulence intensity can be measured from experiments. In recent, micro-particles experiments and tracer gas experiments are most used in investigations of airborne transmission. Romano, et.al [94] simulated the airflow pattern and concentration of airborne particles in an operating theater (OT) by using CFD method. They also conducted an experiment in order to verify the accuracy of simulation results and in their experiment, a six-way aerosol distributor was used to convey the generated aerosol particles; OPC (optical particles counter) equipped with a dilution system was used to measure the particle concentration; A rotating vane anemometer and a thermo-anemometer were used to measure the velocity and temperature respectively. They also validated the simulation result by comparing the data measured from the experiment and found that the experimental and numerical data were well coincided (Error is less than 2% for temperature and 10% for velocity). The value of mean absolute percentage error for particle concentration is 42% though, the experimental curve and the numerical curve are similar in changing trends. Therefore, experiments involving particle-fluid flow are more suitable for qualitative analysis, because it is hard to accurately control conditions such as temperature, pressure, stable velocity of flow.

Zhou, et.al [95] established a model which can be used to predict the distribution of negative ions produced by the air ionizer and the efficiency of this device. In their experiment, an emission system consisting of a compressor and nebulizer was used to compress the filtered air and aerosolize the J o u r n a l P r e -p r o o f bacteria; An ion counter was used to test the emission concentration. In order to present their experiment clearly, the installed experimental system is shown below in Fig. 6 : Fig. 6 The detailed experimental setup [82] The objective of the experiment carried out in this work was to measure the susceptibility Besides, it was proved that the bacterial load in the shower air will increase while turning on the shower spray. The effect of droplet velocity and distribution on aerosolized bacterial groups was not given this study, more, the parameter of shower such as water temperature, nuzzle structures should be also considered in the experiment as well.

Choi, et.al [97] classified the airborne particle according to their optical properties by using experimental methods. Ink-jet aerosol generator (IJAG) was used to generate, dry the airborne particle, the light-scattering signal was used to estimate the correlation value in the classification analysis of airborne particles. The correlation value proposed in this work is helpful for particle detection and classification though, how to apply this method to detect other airborne pathogens with more complicated biological characteristics is required to be furthered. Mei (1) Conveyed air from experiment needs to be filtered;

(2) Particles should be uniformly delivered.

J o u r n a l P r e -p r o o f Experiments to analyzed the particle are useful for understanding the motion law of it. However, it is difficult to massively measure the characteristic of nano-scale particles. The tracer gas method is also a common method in analyzing the pollution diffusion and airflow patterns. Tracer gas can be mixed with air without any changes and it can be easily detected because of special physical characteristics. Helium, nitrogen, argon and carbon dioxide are always chosen to carry out the experiment as a tracer gas. Gao, et.al [102] combined the use of experiment and CFD method to study airborne transmission in different flats of a high-rise building and to verify their simulation, the data of tracer gas experiment from Denmark Aalborg University [103] is used. The analysis of this work is comprehensive by illustrating the transmission mechanism of the airborne virus and how to control virus transmission in a high building based on this investigation is needed to be furthered.

To investigate airborne transmission between horizontal adjacent units, Wu, et.al [104] analyzed influence factors of transmission route especially the contribution of wind force and thermal buoyancy force and found from the result that the wind force is the main driving force to affect the inter-unit dispersion. The experiment conducted in this work is conducted in a slab-type building in Hongkong, SF 6 was used as the tracer gas and injected by the air samples; CO 2 was used to calculate the ventilation rate and monitored by TSI Q-Trak and CO 2 Sensor. Although the spread risk may be overestimated in the analysis because the crack of the door and windows can cause the pathogens aerosol deposit, this work still provides a valuable study in identifying the possible transmission route of the airborne.

Ai, et.al [105] used a tracer gas (NO 2 ) experiment to examine the characteristics of airborne transmission of the exhaled droplet between two people in an experimental room. Two manikins were used to represent an exposed people and an infected people; Air velocity was measured by the Swema 3000 omnidirectional anemometer; PT100 sensor was used to monitor the air temperature; To test the tracer gas concentration, a Faster Concentration Meter (FMC) and INNOVA Multi-gas sampler and Monitor are used. This work has indicated an interaction between exhaled gas and supply flow and analyzed the impact of these factors on infection risk for an exposed person facing an infectious person.

Although the experiment carried out in this work was based on a steady-state condition without taking the impact factor of time into consideration, it provided an effective method for researches afterward. (1) Culturing and filtering the suitable bacteria;

(2) Aerosolizing the bacteria particles and conveying into measuring environment;

(3) Analyzing the airborne transmission of E. coli by using PCR.

And the flow chart given by them is shown below in Fig. 7 : Fig.7 Experiment process of tracing bacteria [110] It will be more persuasive if this process can be carried out in an experiment of researches by using the tracer gas method or particle experiment. However, it will also increase the risk in conducting experiments if the bacteria or virus are highly infectious.

Overall, both the particle experiment and tracer gas experiment can help people understand the process of pathogen transmission, moreover, it provides crucial information for CFD users. On the one hand, the information including experimental data can be used as boundary conditions in CFD simulation; On the other hand, the results of the experiment can be quantitively or qualitatively verified to ensure the accuracy of CFD simulation. Therefore, designing an effective experiment in analyzing pathogen transmission is necessary, it makes the simulation result more convincing.

J o u r n a l P r e -p r o o f

Transmission of pathogens can be different in various spaces and when the epidemic outbreaks caused by infectious pathogens, hospitals will become a high-risk place and may lead to a second infection. How to control the pathogen in hospitals by using an effective ventilation system becomes a great concern. Kao et.al [111] [112] They used the tracer gas NO 2 to replace the viral gas emitted from the patient and simulated three cases under different volumes of supplied air and exhausted air, the simulation results presented the diffusion process of tracer gas as in Fig. 9 : Fig. 9 The simulation of tracer gas diffusion [112] In the same year, this research group studied a similar topic by using the tracer gas and CFD method. In this analysis, the stack effect of high rise building on airflow is considered and the simulation model is based on the General Hospital K in Korea as shown in Fig.10 . Fig. 10 The Prince of Wales Hospital and the simulation model of it [113] They have simulated the spread of tracer gas in the wards of both on the lower floor (5F) and higher floor (15F) to demonstrate the stack effect. Some of the simulation results are shown as shown in Fig. 11 : Figure. 11 Simulation results of the tracer gas transmission in wards of different floors [113] J o u r n a l P r e -p r o o f These researches above mainly investigated pathogen transmission inside the hospital and they are meaningful in protecting patients and hospital staff. However, not only pathogen transmission inside the hospital is dangerous, but the pollutant emission from the hospital is also a great concern for public health. Chang et.al [114] by using CFD modeled the atmospheric environment out the hospital and simulated the spread of the viral (SARS) gas emitted from the hospital. The mesh model of simulation is shown in Fig. 12 : Fig. 12 Mesh model of simulation [114] This model was generated by tetrahedral grids; The wind velocity as a boundary parameter was measured by the hot-film probe and anemometry equipment; 16 wind directions were considered in the calculation. Moreover, in order to verify this model, tracer gas was used in the experiment model with a 1:50 scale. The simulation result below in Fig. 13 respectively shows the concentration contour of pollutant gas at both the height of the roof chimney (right) and 1.5m (left) above the ground. Fig. 13 Diffusion of pollutant gas emitted from hospital [114] By the simulation results, they indicated that both the maximum concentration and mean concentration of pollutant gas in small and would not affect residents' health. However, when a large number of SARS patients were arranged in the hospital, it is still a bit risky for people who actives in the high-concentration area on the ground level.

Research works above were mainly focused on the airflow pattern or impact of ventilation on pathogen transmission. However, cross-infection frequently happened in hospitals and should be paid attention to in case studies of pathogen transmission. Based on Eulerian-Lagrangian method, a case study proposed by Wang, et.al [115] has illustrated that the sneezing process from a virus carrier is ventilation is easier to be controlled, hence, it is necessary to ensure safety when emitted the viral gas from the exhausted system from the hospital. Without professional medical equipment, the buildings with high population density such as residential buildings, commercial buildings and campus buildings are in higher infection risk. Yang, et.al [116] studied natural ventilation in teaching buildings by using CFD method. In their investigation, PHOENICS with RANS model was used to simulate the ventilation; The SIMPLE algorithm was used to calculate and PRESTO scheme was used to staggered the pressure interpolation;

The wind profile at inlet boundary of the simulation was determined by the equation of ASHRAE [117] as: 0.22 () ref U y y UH     (27) Through the simulation, they indicated that the ventilation of the teaching building with a "line-type" corridor is better than that of the inside corridor; They have also presented an optimization design for better ventilation in teaching buildings by determining the best wind angle.

Moreover, Cuce, et.al [118] studied the natural ventilation in school buildings based on its working principles and limitation of passive ventilation; In a crowded room, the concentration of volatile organic substances generated by human skin oil is high, Xiong, et.al It can be observed from simulations that particles will spread in flushing because of the turbulence generated by the high speed of flowing water. More, it was obtained that 40%~60% of particles can reach above the toilet seat. The research of this work is meaningful and it was indicated that before flushing, laying down the lid is useful for preventing the virus transmission. More, washing the seat of the toilet is necessary because the floating virus may deposit on the surface of it. This research group has also analyzed the movement of a virus-laden particle in the process of urinal flushing [122] . Without the prevention, over 57% of particles can escape from the urinal and the particle can reach the highest position of 0.84m at only 5.5s . So it is mandatory to wear a mask in public to reduce infection risk.

Furthering this study about virus transmission in the squat toilet by applying the method J o u r n a l P r e -p r o o f proposed in this work is important because, in many places such as China, the use of the squat toilet is higher than that of the sitting toilet in public.

Some investigations of CFD simulations of ventilation or pathogen transmission in the building environment are summarized below in Tab. 6:

It can be obtained from these investigations:

(1) Ventilation is one of the most effective methods to control the pathogens transmission and the reasonable arrangement of the ventilation system is necessary.

(2) The effect of the stack effect should be considered when analyzing the ventilation in high-rise buildings.

(3) Rooms with infected patients need to be diluted with plenty of fresh air.

Traffic vehicles are also dangerous when there are infectious patients. Under the high personnel density and weak ventilation system, it is difficult to control the pathogen such as the airborne virus.

According to this problem, more and more researchers investigated airflow in various kinds of vehicles by using CFD methods. (1) Two particles collisions are mainly considered;

(2) The velocity distribution of each particle exists independently;

(3) The external force does not affect the dynamic behavior of the local collision. There are various models that can be used in the simulation of LBM and these models can be defined by the layout of lattice, some models which are in common use are shown in Fig. 17 (2D) and 

Face masks have been used to prevent virus transmission and it is necessary for the epidemic situation. Li [155] simulated the aerodynamic behavior of a gas mask which consists of two filter layers. Fig. 19 : Fig. 19 Grid model of the gas mask (left) and the flow field of simulation (right) [155] This research indicated that the design of the mask such as the hole properties is important:

Larger hole area and greater hole distribution lead to a lower pressure drop, a smaller dead zone, and so on. Theoretical analysis was mainly studied in this work and it has also provided a reference in designing a sufficient mask. Dbouk, et.al [156] analyzed the role of the mask in preventing the droplet transmission by utilizing OpenFOAM with a combination of the use of turbulence model and porous model. In the simulation model, the mask fitting to the face was considered which is shown as in Fig.20 : 

Turbulent flow in the atmosphere is unsteady due to the changing weather and it is difficult to measure the airborne transmission in the atmospheric environment directly. Although aerodynamics models of airborne transmission based on CFD method have been greatly developed, it is still a big challenge for applying them to the large-scale environment. Seo, et.al [159] presented a method based on meteorological information from web-system that can help for solving this problem.

This research group analyzed the relationship between foot-and-mouth disease (FMD) spread and hourly wind in Anseong. Moreover, they collected the infection data and built a model by using the GIS method. Then, they used a code division multiple access (CDMA) to send the weather data to a weather data acquisition server (WDAS) in every 10 minutes and interlock the data with geographical information. The OpenFOAM code was used to simulate the spread of the airborne virus the simulation result can well describe the virus transmission. The process of the CFD simulation based on web-based forecasting system can be described as below in Fig. 22 : Fig. 22 Detailed process of CFD simulation based on web-based forecasting system

The Web-based forecasting system has been widely used in various cases such as flooding (Li, J o u r n a l P r e -p r o o f et.al [160] ), tourism demand (Song, et.al [161] ), monitoring of marine pollution (Kulawiak, et.al [162] ), etc. However, there are few studies about pathogen transmission based on combing the Web-based forecasting system and CFD method. Hence, more databases of pathogen transmission and meteorological information are needed to develop the Web-based forecasting system in the analysis of pathogen transmission. From investigations summarized in this review, it can be found that ventilation is one of the most effective methods to control pathogen transmission in the air. Different environments require different ventilation systems, the building environment such as teaching building and residential building and the natural ventilation method is the main way to dilute the concentration of the pathogen.

However, in high-risk zones such as hospitals, not only the reasonable ventilation of indoor is required, but also the infectious risk due to emission needs to be considered. Besides, pathogen transmission in J o u r n a l P r e -p r o o f Journal Pre-proof different vehicles is distinct, a proper strategy of ventilation is necessary for transportation especially the airplane and high-speed train with an enclosed environment.

This review also presented some advanced methods for CFD application on pathogen transmission according to recent investigations as:

(1) LBM simulation allows researchers to investigate pathogen transmission from the mesoscale level;

(2) Based on the Porous Media model, researchers can better analyze the transport of pathogens in complex media, such as medical masks, human organs, etc.

(3) Web-based forecasting system can be combined with the CFD method to analyze the transmission of infectious pathogens in the atmospheric environment and predict the cross-regional transmission of pathogens. 

COVID-19): Dashboard Data last updated: 2020/8/10, 3:06pm CEST

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Infection risk of indoor airborne transmission of diseases in multiple spaces

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Risk assessment of airborne infectious diseases in aircraft cabins

Risk of indoor airborne infection transmission estimated from carbon dioxide concentration

A probabilistic transmission dynamic model to assess indoor airborne infection risks. Risk analysis : an official publication of the Society for Risk Analysis

Perspectives on the basic reproductive ratio

Role of air distribution in sars transmission during the largest nosocomial outbreak in hong kong

Influenza virus in human exhaled breath: an observational study

Association of classroom ventilation with reduced illness absence: a prospective study in california elementary schools

Quantifying the routes of transmission for pandemic influenza

A contribution to the mathematical theory of epidemics

Infectious diseases of humans：dynamics and control

Modeling the role of respiratory droplets in Covid-19 type pandemics

Seasonal dynamics of recurrent epidemics

Stability analysis and optimal vaccination of an sir epidemic model

Stability analysis and optimal control of an sir epidemic model with vaccination

Global stability of a delayed sirs epidemic model with saturation incidence and temporary immunity

Epidemics of sirs model with nonuniform transmission on scale-free networks

Phase transitions in some epidemic models defined on small-world networks

Global dynamics of a seir model with varying total population size

Tracking epidemics with google flu trends data and a state-space seir model

Statistical inference in a stochastic epidemic seir model with control intervention: ebola as a case study

Cfd modelling of pathogen transport due to human activity

Integrated Approach of CFD and SIR Epidemiological Model for Infectious Transmission Analysis in Hospital

Numerical and experimental analysis of airborne particles control in an operating theater

Numerical and experimental study on airborne disinfection by negative ions in air duct flow

Droplet distribution and airborne bacteria in an experimental shower unit

Experimental studies on the classification of airborne particles based on their optical properties

Predicting airborne particle deposition by a modified markov chain model for fast estimation of potential contaminant spread

Experimental and cfd study of unsteady airborne pollutant transport within an aircraft cabin mock-up

An assessment of the airborne route in hepatitis b transmission

The airborne transmission of infection between flats in high-rise residential buildings: tracer gas simulation

Short-time airing by single-sided natural ventilation-part 1: Measurement of transient air flow rates

Experimental analysis of driving forces and impact factors of horizontal inter-unit airborne dispersion in a residential building

Airborne transmission of exhaled droplet nuclei between occupants in a room with horizontal air distribution

Influence of human breathing modes on airborne cross infection risk

Person to person droplets transmission characteristics in unidirectional ventilated protective isolation room: the impact of initial droplet size

Airborne transmission and precautions: facts and myths

Experimental and numerical investigation of the wake flow of a human-shaped manikin: experiments by piv and simulations by cfd

A tracing method of airborne bacteria transmission across built environments

Virus diffusion in isolation rooms

The Influence of Ward Ventilation on Hospital Cross Infection by Varying the Location of Supply and Exhaust Air Diffuser Using CFD

The predictions of infection risk of indoor airborne transmission of diseases in high-rise hospitals: Tracer gas simulation

Computational fluid dynamics simulation of air exhaust dispersion from negative isolation wards of hospitals

An air distribution optimization of hospital wards for minimizing cross-infection

Ventilation effect on different position of classrooms in "line" type teaching building

American Society of Heating, Refrigerating and Air Conditioning Engineers, Fundamentals (SI)

Sustainable ventilation strategies in buildings: CFD research. Sustainable Energy Technologies and Assessments

Modeling the time-dependent concentrations of primary and secondary reaction products of ozone with squalene in a university classroom

Prolonged presence of SARS-CoV-2 viral RNA in faecal samples

Can a toilet promote virus transmission? from a fluid dynamics perspective

Virus transmission from urinals

Investigation on the contaminant distribution with improved ventilation system in hospital isolation rooms: Effect of supply and exhaust air diffuser configurations

Bioaerosol deposition in single and two-bed hospital rooms: a numerical and experimental study

Cfd study on the transmission of indoor pollutants under personalized ventilation

Possible role of aerosol transmission in a hospital outbreak of influenza

Spatial distribution of infection risk of sars transmission in a hospital ward

Modelling the performance of upper room ultraviolet germicidal irradiation devices in ventilated rooms: Comparison of analytical and CFD methods

Numerical investigation of airborne infection in naturally ventilated hospital wards with central-corridor type. Indoor and built environment

Novel air distribution systems for commercial aircraft cabins

Identification of contaminant sources in enclosed environments by inverse cfd modeling

Identification of contaminant sources in enclosed spaces by a single sensor

IDENTIFY CONTAMINANT SOURCES IN AIRLINER CABINS BY INVERSE MODELING OF CFD WITH INFORMATION FROM A SENSOR

Current studies on air distributions in commercial airliner cabins

Identification of pollution sources in urban areas using reverse simulation with reversed time marching method

Inverse modeling of indoor instantaneous airborne contaminant source location with adjoint probability-based method under dynamic airflow field

The method of quasi-reversibility : applications to partial differential equations

Experimental and numerical investigation of micro-environmental conditions in public transportation buses

Effects of the window openings on the micro-environmental condition in a school bus

Performance evaluation of air distribution systems in three different china railway high-speed train cabins using numerical simulation

The risk of airborne influenza transmission in passenger cars

Lattice boltzmann method for fluid flows

Lattice bgk models for navier-stokes equation

The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond. The lattice Boltzmann equation for fluid dynamics and beyond

Pore-scale modelling of dynamic interaction between svocs and airborne particles with lattice boltzmann method

Lattice boltzmann method simulation of svoc mass transfer with particle suspensions

Modeling of dynamic deposition and filtration processes of airborne particles by a single fiber with a coupled lattice boltzmann and discrete element method

Lattice boltzmann method and rans approach for simulation of turbulent flows and particle transport and deposition

Multi-block lattice boltzmann simulations of solute transport in shallow water flows

Large-scale oil spill simulation using the lattice boltzmann method, validation on the lebanon oil spill case

Lattice boltzmann simulations of anisotropic permeabilities in carbon paper gas diffusion layers

Drag correlation for dilute and moderately dense fluid-particle systems using the lattice boltzmann method

Lattice boltzmann simulation of liquid water transport in microporous and gas diffusion layers of polymer electrolyte membrane fuel cells

An immersed boundary-lattice boltzmann model for simulation of malaria-infected red blood cell in micro-channel

Aerodynamic behavior of a gas mask canister containing two porous media

On respiratory droplets and face masks

3-D Numerical Simulation of Main Sieve Diaphragm with Three Types Passageway Design in a Gas Mask Canister

The role of porous media in modeling fluid flow within hollow fiber membranes of the total artificial lung

Web-based forecasting system for the airborne spread of livestock infectious disease using computational fluid dynamics

A web-based flood forecasting system for shuangpai region

Developing a web-based tourism demand forecasting system

Interactive visualization of marine pollution monitoring and forecasting data via a web-based gis

The authors are grateful for the research support received from Applied Basic

The authors declared that they have no conflicts of interest to this work as: We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.J o u r n a l P r e -p r o o f

