Analysing the distribution of SARS-CoV-2 infections in schools: integrating model predictions with real world observations

School closures were used as strategies to mitigate transmission in the COVID-19 pandemic. Understanding the nature of SARS-CoV-2 outbreaks and the distribution of infections in classrooms could help inform targeted or precision preventive measures and outbreak management in schools, in response to future pandemics. In this work, we derive an analytical model of Probability Density Function (PDF) of SARS-CoV-2 secondary infections and compare the model with infection data from all public schools in Ontario, Canada between September-December, 2021. The model accounts for major sources of variability in airborne transmission like viral load and dose-response (i.e., the human bodys response to pathogen exposure), air change rate, room dimension, and classroom occupancy. Comparisons between reported cases and the modeled PDF demonstrated the intrinsic overdispersed nature of the real-world and modeled distributions, but uncovered deviations stemming from an assumption of homogeneous spread within a classroom. The inclusion of near-field transmission effects resolved the discrepancy with improved quantitative agreement between the data and modeled distributions. This study provides a practical tool for predicting the size of outbreaks from one index infection, in closed spaces such as schools, and could be applied to inform more focused mitigation measures. Author summaryAt the start of the COVID-19 pandemic, there was huge uncertainty around the risks of SARS-CoV-2 spread in classrooms. In the absence of early predictions surrounding classroom risks, many jurisdictions across countries closed in-person education. There is great interest in adopting a more precision approach to better inform future interventions in the context of airborne virus risks. For this purpose, we need tools that can predict the probability of the size of outbreaks within classrooms along with the impact of interventions including masks, better ventilation, and physical distancing by limiting the number of students per classroom. To this end, we have developed a robust but practical model that yields the probability of secondary infections stemming from index cases occurring within schools on a given day. During model development, the major underlying physical and biological factors that dictate the disease transmission process, both at long-range and close-range, have been accounted for. This enables our model to modify its predictions for different scenarios - and possibly allows its use beyond schools. Finally, the models predictive capability has been verified by comparing its outputs with publicly available data on SARS-CoV-2 diagnoses in Ontario public schools. To our knowledge, this is the first time an analytical model derived from mostly first principles describes real-world infection distributions, satisfactorily. The quantitative match between the theoretical prediction and real-world data offers the proposed model as a possible powerful tool for better-informed precision pandemic mitigation strategies in indoor environments like schools.