## 3 Results
### Risk of Infection  
#### 3.2.1 Rudnick-Milton Model  
The Rudnick-Milton model was run for the daily CO\({}_{2}\) concentration measurements. For each week and for each occupation shift the basic reproduction number was computed. Figure 10 shows an example and Table 4 the results for the analysed weeks. Figure 8: Example of CO\({}_{2}\) measurements at the front and at the back of the classroom. The grey shaded background identifies occupation periods. Figure 9: CO\({}_{2}\) concentration difference between the front and the back of the classroom. (**a**) shows the distribution of the differences. (**b**) shows monthly differences. (**c**) shows monthly results as a percentage of the difference between mean concentration and external concentration, which is assumed to be 380 ppm. Several weeks could not be analysed due to gaps in the measurements. In order to maximise data usage, monthly risk means (\(\overline{P}\)) were computed as  
\[\overline{P}=1-e^{-\frac{\text{i}\overline{I}}{n}\int_{0}^{\overline{I}}\sigma(t )\ dt} \tag{15}\]  
where \(\overline{J}\) is the monthly \(f\) average, computed from all the available measurements during occupation time. The previous expression is an approximation which stands valid while the exponent is small, due to the exponential's non-linearity. For the concentrations registered and the values of the other parameters involved, it was estimated that this introduces \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Weekly Estimation of \(\boldsymbol{R_{\text{o}}}\)**} \\ \hline \hline \multicolumn{5}{c}{**Morning shift**} \\ \cline{2-5}
**Week** & \multicolumn{4}{c}{\(\boldsymbol{q}\) **[quanta/h]**} \\ \cline{2-5}
**09/08–13/08** & **0.26** & **1.26** & **2.46** & **4.71** \\
30/08–03/09** & **0.14** & **0.68** & **1.35** & **2.63** \\
27/09–01/10** & **0.11** & **0.55** & **1.08** & **2.12** \\
25/10–29/10** & **0.06** & **0.30** & **0.60** & **1.14** \\
22/11–26/11** & **0.09** & **0.43** & **0.86** & **1.70** \\
29/11–03/12** & **0.04** & **0.19** & **0.37** & **0.74** \\
06/12–10/12** & **0.05** & **0.27** & **0.54** & **1.07** \\
13/12–17/12** & **0.03** & **0.16** & **0.32** & **0.63** \\ \hline \hline \multicolumn{5}{c}{**Afternoon shift**} \\ \hline \hline \multicolumn{5}{c}{**\(\boldsymbol{q}\) **[quanta/h]**} \\ \cline{2-5}
**Week** & \multicolumn{4}{c}{\(\boldsymbol{1}\)} & **5** & **10** & **20** \\ \hline
09/08–13/08** & **0.16** & **0.80** & **1.57** & **3.06** \\
06/09–10/09** & **0.15** & **0.74** & **1.47** & **2.87** \\
27/09–01/10** & **0.11** & **0.55** & **1.08** & **2.12** \\
04/10–08/10** & **0.09** & **0.43** & **0.86** & **1.69** \\
29/11–03/12** & **0.06** & **0.29** & **0.57** & **1.12** \\
06/12–10/12** & **0.06** & **0.31** & **0.62** & **1.24** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Weekly estimation of the basic reproduction number for different quanta emission rates. Figure 10: Risk results from a weekly measurement in August, for the afternoon shift. CO\({}_{2}\) measurements and the evolution of the probability of infection for different quanta generation rates are shown. The grey shaded background identifies occupation time for the afternoon shift. The coloured boxes detail the probability of infection and the basic reproduction number by the end of the week. relative errors below 10%, which was considered acceptable. Said error is by excess, that is, the predicted risk will be higher, so a conservative approximation is made. The monthly averages obtained are presented in Table 5.  
The results in Tables 4 and 5 show that the risk of airborne infection steadily decreases towards the end of the year. This could be associated with a warmer climate, which would allow for higher ventilation rates while maintaining thermal comfort. Furthermore, it is shown that in general quanta emission rates of up to 5 quanta/h are safe. Depending on the month, quanta emission rates of up to 10 quanta/h could be safe.