Bayesian grey-box modeling of classroom ventilation using CO2 measurements in Canadian primary schools

• Ventilation conditions were evaluated in Canadian classrooms using CO₂ records. • The evaluation combines Bayesian inference and stochastic grey-box modelling. • Pre-calibrated prior assumptions enhanced model estimation accuracy. • Steady-state CO₂ thresholds were estimated to guide ventilation design. Classrooms are among the most vulnerable indoor environments for airborne disease transmission, particularly since the onset of the COVID-19 pandemic. Their high occupant densities, limited ventilation, and frequent close interactions among students and teachers amplify the risk of aerosol infections. Additionally, children’s greater susceptibility to respiratory illnesses further compounds these challenges. This study aims to evaluate classroom ventilation conditions in Canadian primary schools, with an emphasis on per-student ventilation rates derived from CO₂ measurements. By incorporating pre-calibrated prior assumptions for modeling parameters such as students’ CO₂ emission rates, the study examines the performance of a stochastic CO₂-based grey-box model in predicting occupancy and assessing ventilation performance through Bayesian inference. CO₂ field measurement data collected from five Canadian primary school classrooms between April and May 2023 were used to assess the model’s accuracy in estimating occupancy. The validated model was then applied to year-long CO₂ measurements from two Montreal primary school classrooms (2020–2021) to analyze their ventilation conditions. The findings underscore the insufficient supply of clean air across the naturally ventilated classrooms, emphasizing the need for additional air-treatment measures to ensure an adequate clean air supply. Steady-state CO₂ thresholds (C limit , C target , and C ideal ) were established to assist the CO₂-based ventilation designs for managing indoor aerosol exposures. A target of 690 ppm was set for classrooms without clean-air treatment to meet the minimum ECAi level, while a threshold of 1000 ppm was designated for spaces with adequate clean-air supplementation.