VENTILATION | INFECTION RISK Output numbers from the model are for illustration only, but are useful to observe trends and understand absolute magnitudes assume 1:100 people is infected, what is the most likely number of infected people in the 50-person and five-person office? We can think of this problem like pulling balls from a bag given a bag of 990 red balls and 10 white balls, in random draws of 50 balls the most common number of white balls drawn would be zero. Using combination theory, we can predict the most likely number of infectors in a given scenario if we have the scenario occupancy and the CIR (see Figure 1). Even if there is an infector present, the viral load of the infector will vary by several orders of magnitude. Viral load of infector is proportional to the amount of virus they can emit into the air. The more virus exhaled, the greater the concentration of virus in the air, which increases the inhaled dose of susceptible occupants. A dose curve is used to predict what proportion of the susceptible occupants would be infected for a given dose. Because the removal mechanisms are 10-times greater in the 50-person office, the viral emission rate needs to be approximately 10-times larger to give the same probability of infection. Increasing removal mechanisms for example, ventilation and filtration has the effect of shifting the dose curve to the right. For low viral-load infectors, the probability of infection is near zero, and for high viral infectors the dose is near 100% (Figure 2). Proportion of people infected for given viral load 0.7% Figure 3: The red and blue line are curves of the PPI for every given viral load for the five-person and 50-person office scenarios respectively. The area under the curves is the PPI; given values for PPI are illustrative only 0.6% 0.5% Scenario 0.4% Office 5 Office 50 0.3% 0.2% 0.1% 0.0% 106 107 108 109 1010 1011 1012 Total viral load of infectors(s) RNA copies/ml 3% Figure 4: The effect of increasing the per capita ventilation rate in the 50-person and five-person office on the proportion of people infected. All values are illustrative Proportion of population infected 2.5% Scenario Office 5 Office 50 2% 1.5% 1% We have to make some assumptions on viral load to viral emission rate and dose response for these calculations (the limitations are considered in the paper), so output numbers from the model are for illustration only, but are useful to observe trends and understand absolute magnitudes. We can approximately calculate the proportion of a given population, distributed in either five-person or 50-person offices, infected for every given viral load. The proportion of people infected (PPI) proportion of people susceptible x infection probability x probability the infector has the given viral load. This is calculated for each viral load and the resulting graph gives the total proportion of people infected as the area under the graph (Figure 3). For the given assumptions, at a population scale, the transmission risk in a 50-person office is about three-times higher. This isnt a magnitude that would suggest there is advantage in dividing a 50-person office into 10 cellular five-person offices, but this method could help explore which scenarios would lead to better reductions in longrange airborne transmission. Here, for example, improving a poorly ventilated 50-person office would lead to a greater PPI reduction than improving a poorly ventilated five-person office, so could be useful when scheduling which scenarios within a portfolio should be targeted first for improvement. We dont know absolute values, but it is useful to look at trends in PPI when we adjust various parameters. Increasing ventilation of poorly ventilated spaces reduces PPI more than increasing ventilation in an already well-ventilated space (Figure 4). Reducing occupancy or increasing space volume per person also reduce the PPI. This framework also shows that, in many scenarios, there are no infectors or an infector with a viral load so low that they dont emit enough virus to lead to longrange infection of susceptible people. Then, ventilation has little effect. If an infector has a very high viral load, ventilation cant reduce infection rates much because the concentration in the air is too high. A Goldilocks zone exists between these two extremes where the situation is just right for ventilation to have an effect. Then, improving poorly vented spaces has the greatest effect on the reduction of the long-range transmission risk. At all times, the concentration of virus in air is highest in the exhaled puff, so the coffee breath zone (close contact) is where exposure risk is greatest. CJ CHRIS IDDON MCIBSE is chair of the CIBSE Natural Ventilation special interest group 0.5% References: 0% 0 5 10 15 20 Ventilation rate L.s- 1 25 30 1 A population framework for predicting the proportion of people infected by the far-field airborne transmission of SARS-CoV-2 indoors. Building Environment, August 2022 bit.ly/CJNov22C1 There is an open version at bit.ly/CJNov22C2 88 November 2022 www.cibsejournal.com CIBSE Nov 22 pp87-88 Chris Iddon ventilation.indd 88 21/10/2022 19:15