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A widely used analytical model to quantitatively assess airborne infection risk is the Wells-Riley model which is limited to complete air mixing in a single zone. However, this assumption tends not to be feasible (or reality) for many situations. This study aimed to extend the Wells-Riley model so that the infection risk can be calculated in spaces where complete mixing is not present. Some more advanced ventilation concepts create either two horizontally divided air zones in spaces as displacement ventilation or the space may be divided into two vertical zones by downward plane jet as in protective-zone ventilation systems. This is done by evaluating the time-dependent distribution of infectious quanta in each zone and by solving the coupled system of differential equations based on the zonal quanta concentrations. This model introduces a novel approach by estimating the interzonal mixing factor based on previous experimental data for three types of ventilation systems: incomplete mixing ventilation, displacement ventilation, and protective zone ventilation. The modeling approach is applied to a room with one infected and one susceptible person present. The results show that using the Wells-Riley model based on the assumption of completely air mixing may considerably overestimate or underestimate the long-range airborne infection risk in rooms where air distribution is different than complete mixing, such as displacement ventilation, protected zone ventilation, warm air supplied from the ceiling, etc. Therefore, in spaces with non-uniform air distribution, a zonal modeling approach should be preferred in analytical models compared to the conventional single-zone Wells-Riley models when assessing long-range airborne transmission risk of infectious respiratory diseases.

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A novel modified version of the Wells-Riley model was used to estimate the impact of relative humidity (RH) on the removal of respiratory droplets containing the SARS-CoV-2 virus by deposition through gravitational settling and its inactivation by biological decay; the effect of RH on susceptibility to SARS-CoV-2 was not considered. These effects were compared with the removal achieved by increased ventilation rate with outdoor air. Modeling was performed assuming that the infected person talked continuously for 60 and 120 min. The results of modeling showed that the relative impact of RH on the infection risk depended on the ventilation rate and the size range of virus-laden droplets. A ventilation rate of 0.5 ACH, the change of RH between 20% and 53% was predicted to have a small effect on the infection risk, while at a ventilation rate of 6 ACH this change had nearly no effect. On the contrary, increasing the ventilation rate from 0.5 ACH to 6 ACH was predicted to decrease the infection risk by half which is remarkably larger effect compared with that predicted for RH. It is thus concluded that increasing the ventilation rate is more beneficial for reducing the airborne levels of SARS-CoV-2 than changing indoor RH. PRACTICAL IMPLICATIONS: The present results show that humidification to moderate levels of 40%-60% RH should not be expected to provide a significant reduction in infection risk caused by SARS-CoV-2, hence installing and running humidifiers may not be an efficient solution to reduce the risk of COVID-19 disease in indoor spaces. The results do however confirm that ventilation has a key role in controlling SARS-CoV-2 virus concentration in the air providing considerably higher benefits. The modified model developed in the present work can be used by public health experts, engineers, and epidemiologists when selecting different measures to reduce the infection risk from SARS-CoV-2 indoors allowing informed decisions concerning indoor environmental control.

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This paper applies the Rudnick and Milton method through the dynamic evaluation of the probability of airborne contagion, redefining all parameters and variables in discretized form. To adapt the calculation of the risk of contagion to real needs, scenarios are used to define the presence of people, infected subjects, the hourly production of the quanta of infection, and the calculation of the concentration of CO2 produced by exhalation in the air. Three case studies are discussed: a school, an office, a commercial activity. Complex scenarios include environmental sanitization, a variable number of people, and the possibility of simulating work shifts. The dynamic evaluation of the quanta of infection is also estimated, not foreseen by the Rudnick and Milton model, and involves updating the average values of the equivalent fraction of the indoor air with an improvement in the accuracy of the calculation due to the reduction of improper peaks of the stationary variables.

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Many schools and universities have seen a significant increase in the spread of COVID-19. As such, a number of non-pharmaceutical interventions have been proposed including distancing requirements, surveillance testing, and updating ventilation systems. Unfortunately, there is limited guidance for which policy or set of policies are most effective for a specific school system. We develop a novel approach to model the spread of SARS-CoV-2 quanta in a closed classroom environment that extends traditional transmission models that assume uniform mixing through air recirculation by including the local spread of quanta from a contagious source. In addition, the behavior of students with respect to guideline compliance was modeled through an agent-based simulation. Estimated infection rates were on average lower using traditional transmission models compared to our approach. Further, we found that although ventilation changes were effective at reducing mean transmission risk, it had much less impact than distancing practices. Duration of the class was an important factor in determining the transmission risk. For the same total number of semester hours for a class, delivering lectures more frequently for shorter durations was preferable to less frequently with longer durations. Finally, as expected, as the contact tracing level increased, more infectious students were identified and removed from the environment and the spread slowed, though there were diminishing returns. These findings can help provide guidance as to which school-based policies would be most effective at reducing risk and can be used in a cost/comparative effectiveness estimation study given local costs and constraints.

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In this paper we develop a simple model of the inhaled flow rate of aerosol particles of respiratory origin i.e. that have been exhaled by other people. A connection is made between the exposure dose and the probability of developing an airborne disease. This allows a simple assessment of the outdoor versus indoor risk of contamination to be made in a variety of meteorological situations. It is shown quantitatively that for most cases, the outdoor risk is orders of magnitude less than the indoor risk and that it can become comparable only for extremely specific meteorological and topographical situations. It sheds light on various observations of COVID-19 spreading in mountain valleys with temperature inversions while at the same time other areas are much less impacted.

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Airborne transmission is a recognized pathway of contagion; however, it is rarely quantitatively evaluated. The numerous outbreaks that have occurred during the SARS-CoV-2 pandemic are putting a demand on researchers to develop approaches capable of both predicting contagion in closed environments (predictive assessment) and analyzing previous infections (retrospective assessment). This study presents a novel approach for quantitative assessment of the individual infection risk of susceptible subjects exposed in indoor microenvironments in the presence of an asymptomatic infected SARS-CoV-2 subject. The application of a Monte Carlo method allowed the risk for an exposed healthy subject to be evaluated or, starting from an acceptable risk, the maximum exposure time. We applied the proposed approach to four distinct scenarios for a prospective assessment, highlighting that, in order to guarantee an acceptable risk of 10-3 for exposed subjects in naturally ventilated indoor environments, the exposure time could be well below one hour. Such maximum exposure time clearly depends on the viral load emission of the infected subject and on the exposure conditions; thus, longer exposure times were estimated for mechanically ventilated indoor environments and lower viral load emissions. The proposed approach was used for retrospective assessment of documented outbreaks in a restaurant in Guangzhou (China) and at a choir rehearsal in Mount Vernon (USA), showing that, in both cases, the high attack rate values can be justified only assuming the airborne transmission as the main route of contagion. Moreover, we show that such outbreaks are not caused by the rare presence of a superspreader, but can be likely explained by the co-existence of conditions, including emission and exposure parameters, leading to a highly probable event, which can be defined as a "superspreading event".

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Airborne transmission is a pathway of contagion that is still not sufficiently investigated despite the evidence in the scientific literature of the role it can play in the context of an epidemic. While the medical research area dedicates efforts to find cures and remedies to counteract the effects of a virus, the engineering area is involved in providing risk assessments in indoor environments by simulating the airborne transmission of the virus during an epidemic. To this end, virus air emission data are needed. Unfortunately, this information is usually available only after the outbreak, based on specific reverse engineering cases. In this work, a novel approach to estimate the viral load emitted by a contagious subject on the basis of the viral load in the mouth, the type of respiratory activity (e.g. breathing, speaking, whispering), respiratory physiological parameters (e.g. inhalation rate), and activity level (e.g. resting, standing, light exercise) is proposed. The results showed that high quanta emission rates (>100 quanta h-1) can be reached by an asymptomatic infectious SARS-CoV-2 subject performing vocalization during light activities (i.e. walking slowly) whereas a symptomatic SARS-CoV-2 subject in resting conditions mostly has a low quanta emission rate (<1 quantum h-1). The findings in terms of quanta emission rates were then adopted in infection risk models to demonstrate its application by evaluating the number of people infected by an asymptomatic SARS-CoV-2 subject in Italian indoor microenvironments before and after the introduction of virus containment measures. The results obtained from the simulations clearly highlight that a key role is played by proper ventilation in containment of the virus in indoor environments.

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