## 4 Implementation of the Risk Index  
### Hazard (H)  
The significance of carbon dioxide (CO\({}_{2}\)) levels within IAQ is widely recognized, often serving as an indicator for ventilation rates [11; 37]. These CO\({}_{2}\) concentrations are indicative of IAQ acceptability and, for this reason, the prevailing likelihood of exceeding predetermined CO\({}_{2}\) thresholds in a classroom will be here considered as the hazard [H] of the developed risk index. Note that in this case, the H is not intended to precisely predict how CO\({}_{2}\) levels will evolve under specific conditions and moment but rather to identify those classrooms with the highest potential for CO\({}_{2}\) concentration under the worst circumstances and boundary conditions possible. Indoor CO\({}_{2}\) levels are primarily influenced by two main variables: (1) the generated CO\({}_{2}\) within a confined space [H\({}_{\text{co2}}^{1}\)], and (2) the potential inflow of outdoor CO\({}_{2}\) concentrations [H\({}_{\text{co2}}^{2}\)], both necessitating the consideration of several factors to assess this hazard (H). The first variable [H\({}_{\text{co2}}^{1}\)] considers factors including (a) the rate at which occupants generate CO\({}_{2}\) within a confined space [CO\({}_{2}^{\text{R}}\)], based on their (b) age [y] and (c) level of activities [ac], and (d) the number of potential occupants [O]. In this study, the variable [ac] (expressed in dimensionless units of the metabolic equivalent of task (met)) represents the ratio of human energy expenditure for a specific physical activity to the basal metabolic rate. For reference, Table 1 presents selected levels of activity and their corresponding generalized average ac values, based on [37]. Note that these values are not disaggregated by age or sex. \begin{table}
\begin{tabular}{c c} \hline
**Description of Level of Activity** & _ac-Level of Activity (Met)_ \\ \hline Resting or sleeping & 0.95 \\ Reclining or sitting calmly & 1.0–1.3 \\ Standing still or sitting while reading, writing, or typing & 1.3 \\ Sitting tasks with minimal exertion & 1.5 \\ Standing tasks with minimal exertion (e.g., store clerk, filing) & 3.0 \\ Walking at a very slow pace (\(<\)2 mph) on a flat surface & 2.0 \\ Walking at a moderate pace (2.8–3.2 mph) on a flat surface & 3.5 \\ Light to moderate calisthenics & 2.8 to 3.8 \\ Moderate effort cleaning or sweeping & 3.8 \\ Dancing—aerobic to general & 7.8 to 7.3 \\ \hline \end{tabular}
\end{table} 
Table 1: Levels of activity and their corresponding ac values according to [37]. In order to facilitate the calculation of H\({}_{\text{co2}}^{1}\), Table 2 contains CO\({}_{2}\) generation rates [CO\({}_{2}^{\text{R}}\)] for a number of different levels of activity [ac] values over a range of ages [y] according to [37]. These values are most accurate, but still inherently approximate, when applied to a group of individuals and will not generally be accurate for a single individual. Using the CO\({}_{2}^{\text{R}}\) generation rate values, the Generation Rate Index [I\({}_{\text{CO}_{2}^{\text{R}}}\)] is directly retrieved by rescaling the latter and multiplying it by 12.5. Based on these values and to qualitatively assess the impact of H\({}_{\text{co2}}^{1}\) in H, Equation (1) was developed. This equation tends to allocate higher and lower values to scenarios with increased and reduced risk, respectively, abstaining from embodying a particular physical implication, by multiplying the occupancy [O] by the previously defined Generation Rate Index [I\({}_{\text{CO}_{2}^{\text{R}}}\)]. \[\text{H}_{\text{co2}}^{1}=\sum\sum\left(\text{O}_{\text{y,ac}}\right)\left( \text{I}_{\text{CO}_{2}^{\text{R}}}\right) \tag{1}\]  
Outdoor air quality CO\({}_{2}\) values may not directly affect indoor CO\({}_{2}\) concentrations, but its impact on building ventilation rates, occupant behaviors, and indoor air quality management strategies can indirectly influence indoor CO\({}_{2}\) levels.