key: cord-298461-tyhtdawb authors: Zhao, L.; Qi, Y.; Luzzatto-Fegiz, P.; Cui, Y.; Zhu, Y. title: COVID-19: Effects of weather conditions on the propagation of respiratory droplets date: 2020-05-25 journal: nan DOI: 10.1101/2020.05.24.20111963 sha: doc_id: 298461 cord_uid: tyhtdawb As the number of confirmed cases of Coronavirus disease 2019 (COVID-19) continues to increase, there has been a rising concern regarding the effect of weather conditions, especially over the upcoming summer, on the transmission of this disease. In this study, we assess the transmission of COVID-19 under different weather conditions by investigating the propagation of infectious respiratory droplets. A comprehensive mathematical model is established to explore their evaporation, heat transfer and kinematics under different temperature, humidity and ventilation conditions. The transmitting pathway of COVID-19 through respiratory droplets is divided into short-range droplet contacts and long-range aerosol exposure. We show that the effect of weather conditions is not monotonic: low temperature and high humidity facilitate droplet contact transmission, while high temperature and low humidity promote the formation of aerosol particles and accumulation of particles with a diameter of 2.5 m or less (PM2.5). Our model suggests that the 6 ft of social distance recommended by the Center for Disease Control and Prevention (CDC) may be insufficient in certain environmental conditions, as the droplet spreading distance can be as long as 6 m (19.7 ft) in cold and humid weather. The results of this study suggest that the current pandemic may not ebb in the summer of the northern hemisphere without proper intervention, as there is an increasing chance of aerosol transmission. We also emphasize that the meticulous design of building ventilation systems is critical in containing both the droplet contact infections and aerosol exposures. ABSTRACT: As the number of confirmed cases of Coronavirus disease 2019 (COVID- 19) continues to increase, there has been a rising concern regarding the effect of weather conditions, especially over the upcoming summer, on the transmission of this disease. In this study, we assess the transmission of COVID-19 under different weather conditions by investigating the propagation of infectious respiratory droplets. A comprehensive mathematical model is established to explore their evaporation, heat transfer and kinematics under different temperature, humidity and ventilation conditions. The transmitting pathway of COVID-19 through respiratory droplets is divided into short-range droplet contacts and long-range aerosol exposure. We show that the effect of weather conditions is not monotonic: low temperature and high humidity facilitate droplet contact transmission, while high temperature and low humidity promote the formation of aerosol particles and accumulation of particles with a diameter of 2.5 μm or less (PM2.5). Our model suggests that the 6 ft of social distance recommended by the Center for Disease Control and Prevention (CDC) may be insufficient in certain environmental conditions, as the droplet spreading distance can be as long as 6 m (19.7 ft) in cold and humid weather. The results of this study suggest that the current pandemic may not ebb in the summer of the northern hemisphere without proper intervention, as there is an increasing chance of aerosol transmission. We also emphasize that the meticulous design of building ventilation systems is critical in containing both the droplet contact infections and aerosol exposures. Coronavirus disease 2019 (COVID- 19) is an ongoing global pandemic with more than 5 million confirmed cases and over 0.3 million deaths as of May 23th,(1) within six months since the first case was identified. The disease is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). (2) (3) (4) (5) One major challenge for the effective containment and mitigation of the virus before vaccines are available is its high transmissibility. (6) (7) (8) (9) The basic reproduction number R0, which measures the average secondary infections caused by one infectious case, for COVID-19 has a mean value of 3.28 and may rise to as high as 6.32 without proper public health interventions,(10-12) a sobering value compared to R0 = 1.4-1.7 for influenza and R0 = 1-3 for the severe acute respiratory syndrome (SARS). (13, 14) Therefore, a detailed and quantitative understanding of the transmission mechanisms of SARS-CoV-2 under realistic circumstances is of paramount importance, particularly as many countries start to ease their mobility restrictions. Among known transmitting pathways of SARS-CoV-2, transmission via respiratory droplets is believed to be a primary mode, based on previous studies on SARS (15) and influenza (16) . As many as 40,000 respiratory droplets can be generated by sneezing, coughing and even normal talking, with initial speeds ranging from a few meters per second up to more than a hundred meters per second. (17) (18) (19) These respiratory droplets are expelled from our upper respiratory tracts (URTs) and serve as potential pathogen carriers. (20) Extensive studies have been conducted to investigate the formation, (21, 22) spreading, (18) (19) (20) 23) and infectivity (24, 25) of respiratory droplets. Models to predict the infection probability under different circumstances have been developed as well. (26) (27) (28) These past studies suggest that both aerodynamics and the heat and mass exchange process with the environment can determine the mode and the effectiveness of virus propagation during the travel of respiratory droplets. While large droplets usually settle onto a surface within a limited distance due to gravity, smaller droplets evaporate rapidly to form aerosol particles that are able to carry the virus and float in air for hours. (28, 29) Under certain weather conditions, how far can the virus carriers travel on average? What fraction of droplets will turn into aerosol particles? What role do the HVAC and air conditioning systems play in virus propagation? Quantitative answers to these practical questions can provide urgently needed guidance to both policy makers and the general public, e.g. on social distancing rules. In fact, there have already been intensive ongoing debates about the potential impact of weather conditions on the COVID-19 pandemic. Environmental parameters, such as temperature and humidity, can profoundly affect the survival and transmission of the virus, as well as the immune function and social behaviors of the hosts.(20-23) As a result, the spreading of SARS and influenza have shown strong dependence on seasonality: SARS vanished in the summer of 2003 and the massive infection of influenza mostly happens in wintertime. However, whether COVID-reproductive number R0 for 100 Chinese cities and argued that high temperature and high humidity reduced the transmission of COVID-19. (33) In contrast, another research by Kissler et al (34) assumed similar seasonality of COVID-19 with human coronavirus OC43 (HCoV-OC43) and HCoV-HKU1. They highlighted potentially recurrent seasonal outbreaks of COVID- 19 until 2024 in spite of the immunity gained from vaccination. It is clear that a comprehensive study on the interactions between weather conditions and the propagation of SARS-CoV-2-containing respiratory droplets can help resolve some of the controversies. This study investigates the influence of weather conditions including temperature, humidity and wind velocity, on the transmission of SARS-CoV-2-containing respiratory droplets. We integrate aerodynamics, evaporation, heat transfer and kinematic theories into a mathematical model to predict the spreading capabilities of COVID-19 in different weather conditions. We expanded the modeling framework developed by Wells,(29) Kukkonen et al (35) and Xie et al(23) by discussing Brownian motion, considering residual salt and incorporating kinematic analysis of aerosol particles. As shown in Figure 1 , the transmission of COVID-19 through respiratory droplets is categorized into two modes: droplet contact and exposure to aerosol particles. We first focus on the effect of temperature and relative humidity on these two modes of disease transmission. Our results suggest that high temperature and low humidity promote the formation of aerosol particles, while low temperature and high humidity promote droplet contact transmission. Although social distancing has been proven effective in slowing down COVID-19 transmission, the 6 feet of physical distance recommended by the Centers for Disease Control and Prevention (CDC) turns out to be insufficient in eliminating all possible droplet contacts. In some extremely cool and humid weather conditions, the droplet spreading distance may reach as far as 6 m (19.7 feet). We suggest that the current pandemic may not ebb over the summer without continuous and proper public health intervention, because (1) in hot and dry weather, respiratory droplets more easily evaporate into aerosol particles capable of long-range transmission; (2) infectious PM2.5 that can infiltrate deeply into our lung has a longer suspension time in hot and dry weather; (3) many public spaces implement air-conditioning systems that can still operate at temperature and humidity setpoints that favor droplet transport. Our results also demonstrate that ventilation has both favorable and adverse consequences. On one hand, ventilation to outdoor air can effectively dilute the accumulation of infectious aerosol particles; on the other hand, improper design of ventilation systems may void the effort of social distancing by expanding the traveling All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 25, 2020. . https://doi.org/10.1101/2020.05.24.20111963 doi: medRxiv preprint distance of pathogen-carrying droplets and aerosols. Last but not least, we emphasize that the effect of weather on COVID-19 transmission is not monotonic. To curb the spread of this disease and avoid possible resurgent waves of infections, we advise that flexible public health measures should be taken depending on detailed environmental conditions. After being exhaled by a patient, respiratory droplets with various sizes will travel and simultaneously evaporate in the ambient environment. Small-sized droplets dry immediately to form a cloud of aerosol particles. These particles will suspend in the air for a significant amount of time. Largesized droplets can reach a limited distance and fall to the ground due to gravity. We define Lmax as the maximum horizontal distance that droplets can travel before they either become dry aerosol particles or descend below the level of another person's hands, i.e., H/2 from the ground, where H is the height of another person. To understand the evolution of respiratory droplets, we first examine a single respiratory droplet expelled from the URT of a patient. Upon being released, the droplet begins to exchange heat and mass with the environment while moving under various forces (gravity Fg, buoyancy Fb and air drag Fd in Figure 1 ). As described earlier, respiratory droplets will evolve into two categories depending on their initial diameter d0: 1) aerosol particles made up of residues (salts, pathogens, enzymes, cells, and surfactants) after the dehydration of small droplets. Here we name those solid particles originating from small droplets as aerosol particles to distinguish from the airborne aerosol defined by the World Health Organization (WHO),(36) which employed a straight All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 25, 2020. . https://doi.org/10.1101/2020.05.24.20111963 doi: medRxiv preprint 5 μm cut-off. Generally, the aerosol particles in this study range from 1 μm to 10 μm and share similar dynamic behaviors and impact on human respiratory systems. Likewise, such viruscarrying aerosol particles can lead to airborne transmission of COVID-19 once being inhaled (37, 38) . Because of their long suspension time in air, they have the potential of achieving long-range infection(32) Generally wearing a face mask can effectively lower the chance of transmission via aerosol particles. 2) large droplets that transmit the disease by contact. The infection range of these droplets is limited to a relatively short distance, because they are more sensitive to gravity and can settle on a surface before drying. If these droplets happen to land on the upper body of another person, viruses can easily enter their URTs by face-touching and eye-rubbing. This type of virus transmission can be prevented by practicing social distancing. We define a critical distance Lmax as the maximum horizontal distance that all respiratory droplets can travel before they either shrink to suspending aerosol particles or descend to the level of another person's hands (H/2 from the ground, where H is the person's height). Beyond Lmax, an individual will be completely clear of falling droplets (category 2), but can still be exposed to long-range aerosol particles (category 1), as shown in Figure 1 . The general modeling framework can be briefly summarized as: (1) the evaporation is a mass transport process dominated by the difference in the vapor pressure between the droplet surface and the ambient environment; (2) the temperature of the droplet is solved by considering heat transfer between the droplet and the environment via evaporation, radiation and convection; (3) gravity, buoyancy and drag contribute to the displacement of droplets/aerosol particles; (4) all thermophysical properties of the droplet and air are dependent on temperature and humidity. To improve upon previous models, (23, 29, 35) we further analyzed the effect of Brownian motion, considered the effect of residue salts in respiratory droplets on the terminal particle size, and incorporated a kinematic analysis on aerosol particle transport and deposition. We find that the Brownian motion becomes significant only for droplets with diameters smaller than 0.5 μm. The expected fluctuations of a 1 μm particle caused by Brownian motion is limited to 0.03 m in the life of a droplet. Therefore, we eventually neglected the Brownian force in formulating the kinematic equation. After complete evaporation of the droplets, the analysis on the residue aerosol particle was continued by solving its transport and deposition using kinematic equations. Detailed model formulations, including evaporation model, heat transfer model, kinematic analysis, and validations of our model can be found in the Supporting Information. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 25, 2020. . https://doi.org/10.1101/2020.05.24.20111963 doi: medRxiv preprint Key parameters considered in the model include the distribution of initial droplet size d0, initial velocity v0, environmental temperature T ∞ , relative humidity RH, air velocity Vair, whose values are given here. The initial velocity v0 of droplets was taken as 4.1 m/s for speaking. (39) We also calculated the sneezing mode (v0=100 m/s) and the results are shown in the Supporting Information. For the subsequent sections, we choose to focus on speaking mode to mimic a real social distancing situation where people keep a reasonable physical distance and only sneeze/cough into a tissue or their elbow. The probability distribution of initial droplet diameter d0 is from a previous experimental work by Duguid.(40) , listed in the Supporting Information. The initial temperature T0 of exhaled droplets was set to be 33 ℃. (41) For the environment, we used an average Vair = 0.3 m/s in horizontal direction as the wind speed for an indoor environment, (42) and varied the wind speed from 0-3 m/s when analyzing the effect of ventilation and wind. In order to explore the effects of weather conditions, environmental temperature T ∞ and relative humidity RH were varied from 0-42 ℃ and 0-0.92, respectively. Figure S5 (a) shows that the droplet diameter shrinks over time and that droplets smaller than 20 μm evaporate within 1 s. Figure S5 (b) demonstrates that all the droplets cool to the wet bulb temperature Twb in less than 1 second due to the latent heat required by evaporation. The trajectory of a droplet is analyzed in terms of the vertical distance Lz (Figure 2 (a)) and horizontal distance Lx (Figure 2 (b)) that the droplet can travel before it either completely dries or descends to the level of another person's hand (H/2). Here we set H to be the average height of American adults (1.75 m). Figure 2 (a) shows that droplets with diameter smaller than 73.5 μm can completely dehydrate into aerosol particles and therefore only descend a vertical distance less than H/2. Droplets larger than 73.5 μm fall below the level of hands (H/2). They are less likely to transmit the disease and we do not consider them dangerous. Therefore, we used a plain cut-off of Lz = H/2 for all droplets falling below that. A critical droplet diameter dc can be defined by identifying the initial diameter below which droplets can fully evaporate before descending to the hands. Figure 2 (b) reveals that the maximum of Lx occurs at d0 = dc as well. As shown in Figure 2 (c), for d 1 µm); 2) the deviation of those particles from their original induced by Brownian motion is negligible. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 25, 2020. . https://doi.org/10.1101/2020.05. 24.20111963 doi: medRxiv preprint To validate our model, we firstly investigated the evaporation of stagnant water droplets (T0 = 9 ℃) evaporating in dry air (T ∞ = 25 ℃, RH = 0) and compared the results to an experimental work by Ranz and Marshall.(5) As shown in Figure S2 Figure S2 (b). Generally, our results agree well with and the overshoot of our model results may be attributed to the small differences in water and air parameters that were adopted. The size and distribution of speech droplets, i.e., respiratory droplets expelled by speaking, are taken from a work published by J. P, Duguid.(4) Here we present a probability density distribution of different initial diameters of speech droplets in Figure S3 . All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 25, 2020. . https://doi.org/10.1101/2020.05.24.20111963 doi: medRxiv preprint Figure S3 . Probability density distribution of the initial diameter of speech droplets Once the droplet has dried out, as-formed aerosol particles will suspend in air for a long time and eventually fall on the ground due to gravity. If there is no airflow in vertical direction, the vertical movement of aerosol particles is solely controlled by gravity, buoyancy and air drag. Because the downward velocity vz of droplet nuclei are usually on the order of 10 -5 -10 -4 m/s, Re<<1 and therefore we can assume a Stokes flow around the droplet nuclei. (S16) where mr is the mass and r is the radius of the droplet nucleus. Equation S16 can be solved with initial condition of vz = v0 at t = 0, where vt is the terminal velocity of the droplet. is the time constant. (S18) ve = g (1-⍴a/⍴) is the falling velocity of the aerosol particle by assuming gravity is entirely balanced by buoyancy and air drag. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 25, 2020. . https://doi.org/10.1101/2020.05.24.20111963 doi: medRxiv preprint We first examine the evaporation dynamics of a sneezing droplet (T0 = 33 ℃, v0 = 100 m/s) in T ∞ = 20 ℃ and RH = 0.4. The time-dependent characteristics of an evaporating sneezing droplet is shown in Figure S4 . Figure S4 . Evolution of (a) droplet diameter and (b) droplet temperature of a sneezing droplet. The initial condition of the droplet is taken as T0 = 33 ℃ and v0 = 100 m/s. The environment is set to be T ∞ = 20 ℃, RH = 0.4 and Vair = 0 m/s. Figure S4 demonstrates the strong dependence of droplet evaporation dynamics on the initial diameter of a sneezing droplet. In Figure S4 (a), the diameter of a small droplet (d0 = 50 μm) experiences a rapid decrease. For a large droplet, the diameter firstly decreases linearly, because the evaporative flux at this point is primarily determined by the vapor pressure difference; eventually its diameter experiences a sharp decrease in that the increasing surface-to-volume ratio further intensifies the evaporation. Figure S4 (b) presents the temperature profile of a droplet during evaporation. Note that the x axis in this figure is in logarithmic scale. Apparently, the temperature of all droplets rapidly decreases to the wet bulb temperature Twb within one second, owing to the large latent heat required to evaporate. Therefore, the effect of heat transfer is not significant on the evaporation dynamics, as the droplet stays at Twb throughout the evaporation process. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. Figure S5 shows the evaporation dynamics of a speech droplet that has a smaller initial velocity. The environment is taken as the typical indoor air, i.e., T ∞ = 23 ℃, RH = 0.5 and Vair = 0.3 m/s. Generally, the speech droplet shares the similar behaviors with the sneezing droplet, as the respiratory droplets are sensitive to air drag and its velocity can decelerate to the wind velocity rapidly. If the concentration of SARS-CoV-2 is constant in all respiratory secretions, then the number of viruses Nv in a respiratory droplet is determined by its size. (S19) where n is the average number per unit volume. Based on the size distribution presented in Figure S3 and J. P, Duguid(4), we calculated the percentage of viral load in each diameter range ( Figure S6 (a)). (S20) All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 25, 2020. Lx for droplets with different initial diameter d0. In order to obtain the distance-dependent viruses that one may receive, we also computed the traveling distance Lx for different d0 and weather conditions ( Figure S6 (b) ). By combining Figure S6 (a) and (b), we are able to plot the distance-dependent viral load in Figure S7 , which characterizes the effectiveness of social distancing at different distances. Figure S7 . Effectiveness of practicing social distancing at different distance All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 25, 2020. . https://doi.org/10.1101/2020.05.24.20111963 doi: medRxiv preprint Figure S6 (b) presents the traveling distance of different droplets at four weather extremes, i.e., cold and humid (T ∞ = 4 ℃, RH = 0.88), cold and dry (T ∞ = 4 ℃, RH = 0), hot and dry (T ∞ = 36 ℃, RH = 0), hot and humid (T ∞ = 36 ℃, RH = 0.88). We find that the horizontal traveling of small droplets (d0 <100 μm) is strongly dependent on weather conditions; however, large droplets are inert and become insensitive to weather change. Since most pathogens exist in large respiratory droplets, the curve of distance-dependent viral load in Figure S7 is not sensitive to weather conditions. Therefore, we only demonstrate the viral load curve under normal indoor conditions (T ∞ = 23 ℃, RH = 0.50, Vair = 0.3 m/s), and a weather-independent criterion can be used for relaxed social distancing. By integrating equation (S17), the suspension time ts that is required for a particle to deposit on the ground can be calculated as: We then calculated the average suspension time tm of PM2.5 under different weather conditions, as shown in Figure S8 (a). Generally, PM2.5 can suspend in air for around 10 hours. We also find that the hot and dry temperature gives rise to a longer suspension time for PM2.5, as shown in Figure S9 (b). The suspension time ts varies dramatically from 4 hours to around 10 hours when the diameter changes from 10 μm to 1 μm. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 25, 2020. . https://doi.org/10.1101/2020.05.24.20111963 doi: medRxiv preprint Figure S8 . Average suspension time of PM2.5 under different weather conditions Assume the percentage of droplets that can turn into PM2.5 in speech droplets is p(d0). dr is the diameter of the aerosol particle after dehydrating. Then the number of PM2.5 that can be produced by constant speaking is ∑ ( 0 ) 0 , where N is the number of produced droplets per second. After ts, the number of the corresponding aerosol particles reaches equilibrium, as the number of newly produced particles is now equal to that of aerosol particles falling on ground. Therefore, the total mass of PM2.5 can be calculated: (S20) In this study, N is equal to 50 droplets per minute.(6) Based on equation S20, the total mass of PM2.5 has been computed under different weather conditions in Figure 3 (d). 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