Predictive and retrospective modelling of airborne infection risk using monitored carbon dioxide

The risk of long range, herein `airborne', infection needs to be better understood and is especially urgent during the current COVID-19 pandemic. We present a method to determine the relative risk of airborne transmission that can be readily deployed with either modelled or monitored CO$_2$ data and occupancy levels within an indoor space. For spaces regularly, or consistently, occupied by the same group of people, e.g. an open-plan office or a school classroom, we establish protocols to assess the absolute risk of airborne infection of this regular attendance at work or school. We present a methodology to easily calculate the expected number of secondary infections arising from a regular attendee becoming infectious and remaining pre/asymptomatic within these spaces. We demonstrate our model by calculating risks for both a modelled open-plan office and by using monitored data recorded within a small naturally ventilated office. In addition, by inferring ventilation rates from monitored CO$_2$ we show that estimates of airborne infection can be accurately reconstructed; thereby offering scope for more informed retrospective modelling should outbreaks occur in spaces where CO$_2$ is monitored. Our modelling suggests that regular attendance at an office for work is unlikely to significantly contribute to the pandemic but only if relatively quiet desk-based work is carried out in the presence of adequate ventilation (i.e. at least 10\,l/s/p following UK guidance), appropriate hygiene controls, distancing measures, and that all commuting presents minimal infection risk. Crucially, modelling even moderate changes to the conditions within the office, or basing estimates for the infectivity of the SARS-CoV-2 variant B1.1.7 current data, typically results in the prediction that for a single infector within the office the airborne route alone gives rises to more than one secondary infection.