## 1 Introduction  
The SARS-CoV-2 pandemic (COVID-19 disease) has had a tremendous global impact. More than six million people have died, there have been massive economic losses, and health systems from around the world have been strained beyond their limits [1]. By now it is well established that SARS-CoV-2 is of airborne transmission, through liquid droplets expelled by infected individuals when breathing, sneezing or coughing. Transmission can either happen through close contact, via larger droplets that follow ballistic trajectories and end up falling, or through smaller aerosolized droplets, which can remain suspended and travel long distances with air drafts [2]. The latter is called the long-range airborne route and has put Indoor Air Quality (IAQ) under the spotlight. In particular, ventilation becomes of paramount importance, as it is the main way of diluting and removing the suspended pathogen from indoor spaces. Moreover, several prominent researchers have insisted in the need for a paradigm shift in how IAQ is conceived, even after the pandemic recedes [3]. For example, risk evaluation has been suggested to become a design method for ventilation systems [4]. Several tools are available for studying indoors ventilation and airborne transmission risk. Perfectly mixed box models have been extensively used for estimating ventilation rates [5, 6, 7, 8, 9] and simple models for quantitatively assessing airborne transmission risk, such as the Wells-Riley approach, have been around for more than 50 years [10; 11]. In the context of the pandemic the interest in these models has increased. New approaches and interesting modifications have been proposed and have enabled the use of these models for risk assessment in public buildings and transport [12; 13; 14; 15; 16]. In particular, there has been substantial interest in studying primary school buildings, as they hold stable populations which stay inside for considerable amounts of time [12; 17]. Furthermore, an important concern regarding school buildings around the world is that many of them lack mechanical ventilation systems, and instead rely on natural ventilation. For these buildings, high ventilation rates during winter might be incompatible with thermal comfort, so the transmission risk could be higher. Many studies have focused on evaluating IAQ in classrooms through measuring carbon dioxide (CO\({}_{2}\)). For example, in [18] IAQ was described in 19 Spanish classrooms through CO\({}_{2}\) measurements. In [19], an aware-raising intervention for improving natural ventilation in school classrooms in Switzerland was evaluated by measuring CO\({}_{2}\) concentrations. Ref. [20] estimated ventilation rates through measuring CO\({}_{2}\) concentrations in five Serbian schools. Ref. [21] evaluated IAQ in ten Australian school classrooms. Indoors temperature, relative humidity, CO\({}_{2}\) concentration and particulate matter concentrations (PM2.5 and PM10) were monitored, and the ventilation rate was calculated from the CO\({}_{2}\) measurements. Measured values were compared to different threshold references, but no risk assessment methods were used. Ref. [22] presented an experimental campaign comprising 17 CO\({}_{2}\) sensors, placed in a representative naturally ventilated primary school classroom. The effectiveness of different ventilation strategies was assessed and practical details regarding CO\({}_{2}\) sensors placement were discussed. The authors concluded that continuous ventilation is needed, instead of intermittent strategies, in order to achieve acceptable air quality. Furthermore, the importance of cross ventilation was highlighted. It should be mentioned that the authors assessed their results in terms of CO\({}_{2}\) concentrations, but did not estimate the airborne transmission risk. This and other studies have mainly focused on either evaluating ventilation rates or airborne contagion risk, but generally do not compare both nor quantitatively analyse recommendations for risk reduction.