Seasonal variation in airborne infection risk in schools due to changes in ventilation inferred from monitored carbon dioxide

The Wells-Riley model revisited: Randomness, heterogeneity, and transient behaviours

The Wells-Riley model has been widely used to estimate airborne infection risk, typically from a deterministic point of view (i.e., focusing on the average number of infections) or in terms of a per capita probability of infection. Some of its main limitations relate to considering well-mixed air, steady-state concentration of pathogen in the air, a particular amount of time for the indoor interaction, and that all individuals are homogeneous and behave equally. Here, we revisit the Wells-Riley model, providing a mathematical formalism for its stochastic version, where the number of infected individuals follows a Binomial distribution. Then, we extend the Wells-Riley methodology to consider transient behaviours, randomness, and population heterogeneity. In particular, we provide analytical solutions for the number of infections and the per capita probability of infection when: (i) susceptible individuals remain in the room after the infector leaves, (ii) the duration of the indoor interaction is random/unknown, and (iii) infectors have heterogeneous quanta production rates (or the quanta production rate of the infector is random/unknown). We illustrate the applicability of our new formulations through two case studies: infection risk due to an infectious healthcare worker (HCW) visiting a patient, and exposure during lunch for uncertain meal times in different dining settings. Our results highlight that infection risk to a susceptible who remains in the space after the infector leaves can be nonnegligible, and highlight the importance of incorporating uncertainty in the duration of the indoor interaction and the infectivity of the infector when estimating risk.

Viral infection transmission and indoor air quality: A systematic review

Respiratory disease transmission in indoor environments presents persistent challenges for health authorities, as exemplified by the recent COVID-19 pandemic. This underscores the urgent necessity to investigate the dynamics of viral infection transmission within indoor environments. This systematic review delves into the methodologies of respiratory infection transmission in indoor settings and explores how the quality of indoor air (IAQ) can be controlled to alleviate this risk while considering the imperative of sustainability. Among the 2722 articles reviewed, 178 were retained based on their focus on respiratory viral infection transmission and IAQ. Fifty eight articles delved into SARS-CoV-2 transmission, 21 papers evaluated IAQ in contexts of other pandemics, 53 papers assessed IAQ during the SARS-CoV-2 pandemic, and 46 papers examined control strategies to mitigate infectious transmission. Furthermore, of the 46 papers investigating control strategies, only nine considered energy consumption. These findings highlight clear gaps in current research, such as analyzing indoor air and surface samples for specific indoor environments, oversight of indoor and outdoor parameters (e.g., temperature, relative humidity (RH), and building orientation), neglect of occupancy schedules, and the absence of considerations for energy consumption while enhancing IAQ. This study distinctly identifies the indoor environmental conditions conducive to the thriving of each respiratory virus, offering IAQ trade-offs to mitigate the risk of dominant viruses at any given time. This study argues that future research should involve digital twins in conjunction with machine learning (ML) techniques. This approach aims to enhance IAQ by analyzing the transmission patterns of various respiratory viruses while considering energy consumption.

Modelling the impact of non-pharmaceutical interventions on workplace transmission of SARS-CoV-2 in the home-delivery sector

OBJECTIVE

We aimed to use mathematical models of SARS-COV-2 to assess the potential efficacy of non-pharmaceutical interventions on transmission in the parcel delivery and logistics sector.

METHODS

We devloped a network-based model of workplace contacts based on data and consultations from companies in the parcel delivery and logistics sectors. We used these in stochastic simulations of disease transmission to predict the probability of workplace outbreaks in this settings. Individuals in the model have different viral load trajectories based on SARS-CoV-2 in-host dynamics, which couple to their infectiousness and test positive probability over time, in order to determine the impact of testing and isolation measures.

RESULTS

The baseline model (without any interventions) showed different workplace infection rates for staff in different job roles. Based on our assumptions of contact patterns in the parcel delivery work setting we found that when a delivery driver was the index case, on average they infect only 0.14 other employees, while for warehouse and office workers this went up to 0.65 and 2.24 respectively. In the LIDD setting this was predicted to be 1.40, 0.98, and 1.34 respectively. Nonetheless, the vast majority of simulations resulted in 0 secondary cases among customers (even without contact-free delivery). Our results showed that a combination of social distancing, office staff working from home, and fixed driver pairings (all interventions carried out by the companies we consulted) reduce the risk of workplace outbreaks by 3-4 times.

CONCLUSION

This work suggests that, without interventions, significant transmission could have occured in these workplaces, but that these posed minimal risk to customers. We found that identifying and isolating regular close-contacts of infectious individuals (i.e. house-share, carpools, or delivery pairs) is an efficient measure for stopping workplace outbreaks. Regular testing can make these isolation measures even more effective but also increases the number of staff isolating at one time. It is therefore more efficient to use these isolation measures in addition to social distancing and contact reduction interventions, rather than instead of, as these reduce both transmission and the number of people needing to isolate at one time.

Safe CO2 threshold limits for indoor long-range airborne transmission control of COVID-19

CO2-based infection risk monitoring is highly recommended during the current COVID-19 pandemic. However, the CO2 monitoring thresholds proposed in the literature are mainly for spaces with fixed occupants. Determining CO2 threshold is challenging in spaces with changing occupancy due to the co-existence of quanta and CO2 remaining from previous occupants. Here, we propose a new calculation framework for deriving safe excess CO2 thresholds (above outdoor level), C t, for various spaces with fixed/changing occupancy and analyze the uncertainty involved. We categorized common indoor spaces into three scenarios based on their occupancy conditions, e.g., fixed or varying infection ratios (infectors/occupants). We proved that the rebreathed fraction-based model can be applied directly for deriving C t in the case of a fixed infection ratio (Scenario 1 and Scenario 2). In the case of varying infection ratios (Scenario 3), C t derivation must follow the general calculation framework due to the existence of initial quanta/excess CO2. Otherwise, C t can be significantly biased (e.g., 260 ppm) when the infection ratio varies greatly. C t can vary significantly based on specific space factors such as occupant number, physical activity, and community prevalence, e.g., 7 ppm for gym and 890 ppm for lecture hall, indicating C t must be determined on a case-by-case basis. An uncertainty of up to 6 orders of magnitude for C t was found for all cases due to uncertainty in emissions of quanta and CO2, thus emphasizing the role of accurate emissions data in determining C t.

Systematic Review of the Key Factors Influencing the Indoor Airborne Spread of SARS-CoV-2

The COVID-19 pandemic due to the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) has been plaguing the world since late 2019/early 2020 and has changed the way we function as a society, halting both economic and social activities worldwide. Classrooms, offices, restaurants, public transport, and other enclosed spaces that typically gather large groups of people indoors, and are considered focal points for the spread of the virus. For society to be able to go "back to normal", it is crucial to keep these places open and functioning. An understanding of the transmission modes occurring in these contexts is essential to set up effective infection control strategies. This understanding was made using a systematic review, according to the Preferred Reporting Items for Systematic reviews and Meta-Analyses statement (PRISMA) 2020 guidelines. We analyze the different parameters influencing airborne transmission indoors, the mathematical models proposed to understand it, and discuss how we can act on these parameters. Methods to judge infection risks through the analysis of the indoor air quality are described. Various mitigation measures are listed, and their efficiency, feasibility, and acceptability are ranked by a panel of experts in the field. Thus, effective ventilation procedures controlled by CO2-monitoring, continued mask wearing, and a strategic control of room occupancy, among other measures, are put forth to enable a safe return to these essential places.

Variations in classroom ventilation during the COVID-19 pandemic: Insights from monitoring 36 naturally ventilated classrooms in the UK during 2021

Seasonal changes in the measured CO2  levels at four schools are herein presented through a set of indoor air quality metrics that were gathered during the height of the COVID-19 pandemic in the UK. Data from non-intrusive environmental monitoring units were remotely collected throughout 2021 from 36 naturally ventilated classrooms at two primary schools and two secondary schools in England. Measurements were analysed to assess the indoor CO2  concentration and temperature . Relative to UK school air quality guidance, the CO2  levels within classrooms remained relatively low during periods of warmer weather, with elevated CO2  levels being evident during the colder seasons, indicating lower levels of per person ventilation during these colder periods. However, CO2  data from the cold period during the latter part of 2021, imply that the per person classroom ventilation levels were significantly lower than those achieved during a similarly cold weather period during the early part of the year. Given that the classroom architecture and usage remained unchanged, this finding suggests that changes in the ventilation behaviours within the classrooms may have altered, and raises questions as to what may have given rise to such change, in a year when, messaging and public concerns regarding COVID-19 varied within the UK. Significant variations were observed when contrasting data, both between schools, and between classrooms within the same school building; suggesting that work is required to understand and catalogue the existing ventilation provisions and architecture within UK classrooms, and that more work is required to ascertain the effects of classroom ventilation behaviours.

Response to the COVID-19 Pandemic in Classrooms at the University of the Basque Country through a User-Informed Natural Ventilation Demonstrator

The COVID-19 pandemic has generated a renewed interest in indoor air quality to limit viral spread. In the case of educational spaces, due to the high concentration of people and the fact that most of the existing buildings do not have any mechanical ventilation system, the different administrations have established natural ventilation protocols to guarantee an air quality that reduces risk of contagion by the SARS-CoV-2 virus after the return to the classrooms. Many of the initial protocols established a ventilation pattern that opted for continuous or intermittent ventilation to varying degrees of intensity. This study, carried out on a university campus in Spain, analyses the performance of natural ventilation activated through the information provided by monitoring and visualisation of real-time data. In order to carry out this analysis, a experiment was set up where a preliminary study of ventilation without providing information to the users was carried out, which was then compared with the result of providing live feedback to the occupants of two classrooms and an administration office in different periods of 2020, 2021 and 2022. In the administration office, a CO2-concentration-based method was applied retrospectively to assess the risk of airborne infection. This experience has served as a basis to establish a route for user-informed improvement of air quality in educational spaces in general through low-cost systems that allow a rational use of natural ventilation while helping maintain an adequate compromise between IAQ, comfort and energy consumption, without having to resort to mechanical ventilation systems.

Risk assessment for long- and short-range airborne transmission of SARS-CoV-2, indoors and outdoors

Preventive measures to reduce infection are needed to combat the COVID-19 pandemic and prepare for a possible endemic phase. Current prophylactic vaccines are highly effective to prevent disease but lose their ability to reduce viral transmission as viral evolution leads to increasing immune escape. Long-term proactive public health policies must therefore complement vaccination with available nonpharmaceutical interventions aiming to reduce the viral transmission risk in public spaces. Here, we revisit the quantitative assessment of airborne transmission risk, considering asymptotic limits that considerably simplify its expression. We show that the aerosol transmission risk is the product of three factors: a biological factor that depends on the viral strain, a hydrodynamical factor defined as the ratio of concentration in viral particles between inhaled and exhaled air, and a face mask filtering factor. The short-range contribution to the risk, present both indoors and outdoors, is related to the turbulent dispersion of exhaled aerosols by air drafts and by convection (indoors), or by the wind (outdoors). We show experimentally that airborne droplets and CO2 molecules present the same dispersion. As a consequence, the dilution factor, and therefore the risk, can be measured quantitatively using the CO2 concentration, regardless of the room volume, the flow rate of fresh air, and the occupancy. We show that the dispersion cone leads to a concentration in viral particles, and therefore a short-range transmission risk, inversely proportional to the squared distance to an infected person and to the flow velocity. The aerosolization criterion derived as an intermediate result, which compares the Stokes relaxation time to the Lagrangian time-scale, may find application for a broad class of aerosol-borne pathogens and pollutants.

A multi-layered strategy for COVID-19 infection prophylaxis in schools: A review of the evidence for masks, distancing, and ventilation

Implications for the academic and interpersonal development of children and adolescents underpin a global political consensus to maintain in-classroom teaching during the ongoing COVID-19 pandemic. In support of this aim, the WHO and UNICEF have called for schools around the globe to be made safer from the risk of COVID-19 transmission. Detailed guidance is needed on how this goal can be successfully implemented in a wide variety of educational settings in order to effectively mitigate impacts on the health of students, staff, their families, and society. This review provides a comprehensive synthesis of current scientific evidence and emerging standards in relation to the use of layered prevention strategies (involving masks, distancing, and ventilation), setting out the basis for their implementation in the school environment. In the presence of increasingly infectious SARS-Cov-2 variants, in-classroom teaching can only be safely maintained through a layered strategy combining multiple protective measures. The precise measures that are needed at any point in time depend upon a number of dynamic factors, including the specific threat-level posed by the circulating variant, the level of community infection, and the political acceptability of the resultant risk. By consistently implementing appropriate prophylaxis measures, evidence shows that the risk of infection from in-classroom teaching can be dramatically reduced. Current studies indicate that wearing high-quality masks and regular testing are amongst the most important measures in preventing infection transmission; whilst effective natural and mechanical ventilation systems have been shown to reduce infection risks in classrooms by over 80%.

An evaluation of the risk of airborne transmission of COVID-19 on an inter-city train carriage

Experiments were conducted in an UK inter-city train carriage with the aim of evaluating the risk of infection to the SARS-CoV-2 virus via airborne transmission. The experiments included in-service CO₂ measurements and the measurement of salt aerosol concentrations released within the carriage. Computational fluid dynamics simulations of the carriage airflow were also used to visualise the airflow patterns, and the efficacy of the HVAC filter material was tested in a laboratory. Assuming an infectious person is present, the risk of infection for a 1-h train journey was estimated to be 6 times lower than for a full day in a well-ventilated office, or 10-12 times lower than a full day in a poorly ventilated office. While the absolute risk for a typical journey is likely low, in the case where a particularly infectious individual is on-board, there is the potential for a number of secondary infections to occur during a 1-h journey. Every effort should therefore be made to minimize the risk of airborne infection within these carriages. Recommendations are also given for the use of CO₂ sensors for the evaluation of the risk of airborne transmission on train carriages.

CO2-measuring dongle

The compact pocketable CO₂-measuring device is built on a small printed circuit board (PCB) with the dimensions of ca. 8.5 × 3 cm. It is plugged into the universal serial bus (USB) port of a personal computer (PC) which serves to provide power and for downloading the measurements. The measurements can be viewed on the computer display where they also can be plotted as a graph to recognize trends. As the level of CO₂ rises indoors when people are present and the air is not exchanged adequately the device can be employed as a personal device for monitoring indoor air quality. This is of particular interest when airborne pathogens might be present such as during the COVID-19 pandemic. The device utilizes a novel compact CO₂ sensor which has only become available commercially recently, and is based on the photoacoustic measuring principle. A graphical user interface on the PC programmed in Python allows easy interaction with the user. A MSP430FR2433 microcontroller on the board controls the sensor and establishes the communication to the software application on the computer. This was facilitated by the choice of Forth as the programming framework for the microcontroller.

Tempo-spatial infection risk assessment of airborne virus via CO2 concentration field monitoring in built environment

The aerosol transmission was academically recognized as a possible transmission route of Coronavirus disease 2019 (COVID-19). We established an approach to assess the indoor tempo-spatial airborne-disease infection risks through aerosol transmission via real-time CO2 field measurement and occupancy monitoring. Compared to former studies, the proposed method can evaluate real-time airborne disease infection risks through aerosol transmission routes. The approach was utilized in a university office. The accumulated infection risk was calculated for three occupants with practical working schedules (from occupancy recording) and one hypothesis occupant with a typical working schedule. COVID-19 was used as an example. Results demonstrated that the individual infection risks diversified with different dwell times and working places in the office. For the three occupants with a practical working schedule, their 3-day accumulated infection risks were respectively 0.050%, 0.035%, 0.027% and 0.041% due to 11.6, 9.0 and 13.8 h exposure with an initial infector percentage of 1%. The results demonstrate that location and dwell time are both important factors influencing the infection risk of certain occupant in built environment, whereas existing literature seldom took these two points into consideration simultaneously. On the contrary, our proposed approach treated the infection risks as place-by-place, time-by-time and person-by-person diversified in the built environment. The risk assessment results can provide early warning for building occupants and contribute to the transmission control of air-borne disease.

A coupled Computational Fluid Dynamics and Wells-Riley model to predict COVID-19 infection probability for passengers on long-distance trains

Coupled Wells-Riley (WR) and Computational Fluid Dynamics (CFD) modelling (WR-CFD) facilitates a detailed analysis of COVID-19 infection probability (IP). This approach overcomes issues associated with the WR 'well-mixed' assumption. The WR-CFD model, which makes uses of a scalar approach to simulate quanta dispersal, is applied to Chinese long-distance trains (G-train). Predicted IPs, at multiple locations, are validated using statistically derived (SD) IPs from reported infections on G-trains. This is the first known attempt to validate a coupled WR-CFD approach using reported COVID-19 infections derived from the rail environment. There is reasonable agreement between trends in predicted and SD IPs, with the maximum SD IP being 10.3% while maximum predicted IP was 14.8%. Additionally, predicted locations of highest and lowest IP, agree with those identified in the statistical analysis. Furthermore, the study demonstrates that the distribution of infectious aerosols is non-uniform and dependent on the nature of the ventilation. This suggests that modelling techniques neglecting these differences are inappropriate for assessing mitigation measures such as physical distancing. A range of mitigation strategies were analysed; the most effective being the majority (90%) of passengers correctly wearing high efficiency masks (e.g. N95). Compared to the base case (40% of passengers wearing low efficiency masks) there was a 95% reduction in average IP. Surprisingly, HEPA filtration was only effective for passengers distant from an index patient, having almost no effect for those in close proximity. Finally, as the approach is based on CFD it can be applied to a range of other indoor environments.

Modeling and experimental study of dispersion and deposition of respiratory emissions with implications for disease transmission

The ability to model the dispersion of pathogens in exhaled breath is important for characterizing transmission of the SARS-CoV-2 virus and other respiratory pathogens. A Computational Fluid Dynamics (CFD) model of droplet and aerosol emission during exhalations has been developed and for the first time compared directly with experimental data for the dispersion of respiratory and oral bacteria from ten subjects coughing, speaking, and singing in a small unventilated room. The modeled exhalations consist of a warm, humid, gaseous carrier flow and droplets represented by a discrete Lagrangian particle phase which incorporates saliva composition. The simulations and experiments both showed greater deposition of bacteria within 1 m of the subject, and the potential for a substantial number of bacteria to remain airborne, with no clear difference in airborne concentration of small bioaerosols (<10 μm diameter) between 1 and 2 m. The agreement between the model and the experimental data for bacterial deposition directly in front of the subjects was encouraging given the uncertainties in model input parameters and the inherent variability within and between subjects. The ability to predict airborne microbial dispersion and deposition gives confidence in the ability to model the consequences of an exhalation and hence the airborne transmission of respiratory pathogens such as SARS-CoV-2.

Air Flow Experiments on a Train Carriage—Towards Understanding the Risk of Airborne Transmission

A series of experiments was undertaken on an intercity train carriage aimed at providing a “proof of concept” for three methods in improving our understanding of airflow behaviour and the accompanied dispersion of exhaled droplets. The methods used included the following: measuring CO2 concentrations as a proxy for exhaled breath, measuring the concentrations of different size fractions of aerosol particles released from a nebuliser, and visualising the flow patterns at cross-sections of the carriage by using a fog machine and lasers. Each experiment succeeded in providing practical insights into the risk of airborne transmission. For example, it was shown that the carriage is not well mixed over its length, however, it is likely to be well mixed along its height and width. A discussion of the suitability of the fresh air supply rates on UK train carriages is also provided, drawing on the CO2 concentrations measured during these experiments.