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Mathematical modeling of ventilation in classrooms as decrease in the risk of contagion by COVID-19

In indoor spaces, there is evidence of the importance of transmission of the SARS-CoV-2 virus by air through aerosols, especially in poorly ventilated conditions. Viruses are exhaled by infected people into respiratory particles with sizes less than 50 microns (microdroplets) that are suspended in the air (aerosols) and can be transported to distances greater than 2 meters within a closed room, such as classrooms. Therefore, in closed school environments, the conditions of occupation and ventilation are essential to determine and minimize the risk of transmission of the virus. There are various techniques to physically assess the air change rate (ACH) in an indoor space or to estimate it indirectly by measuring carbon dioxide (CO2). However, these procedures could be complex for an untrained community or in the absence of a CO2 monitor. The application of mathematical models allows alternatively to evaluate the ventilation conditions from the estimation of ACH or the concentration of CO2 in an intramural space. Some mathematical models were included as part of a guide developed for the evaluation and monitoring of ventilation in school settings. In this work, the application of mass balance models is presented, under conditions of complete mixing, in a classroom in order to estimate ACH from the volume and occupation of the room. Likewise, mathematical expressions are developed to estimate the concentration of CO2 and evaluate the risk of contagion to COVID-19 in situations with and without ventilation. From simple mathematical expressions, it is contributed to the evaluation of the ventilation conditions of classrooms to avoid possible outbreaks of contagion in face-to-face education.