## 3 Results  
In this section, we illustrate the methodology presented in Section 2 on infections and hospitalisation data from the German federal state of Bavaria. We use the infections data from the publicly available database of the German Robert Koch-Institut (RKI) [16] (see Figure 3a). We used daily new infections data from 1 March 2020 to 15 November 2022. The hospitalisation data were aggregated from the \"Sonderlage\" module of the IVENA eHealth system (IVENA) for Mittelfranken [17; 18; 19] and Munich [20; 21; 22]. For our analysis, we used data on daily hospital bed occupancy from 1 April 2020 to 15 November 2022 (see Figure 3b). Matching the underlying data, we choose an observation period from \(t_{0}=1\) April 2022 to \(t_{1}=15\) November 2022 and subsequently go through the three steps in the construction of COVIX. **Step 1:**_Estimation of Hospitalisation Rates \(k_{N}(t)\) and \(k_{ICU}(t)\)_  
**Step 2:**_Estimation of Relative Infections \(I_{rel}(t,t_{ref})\)_  
Given the estimates for the hospitalisation rates in Figure 4, we chose two reference dates, \(t_{ref}=21\) December 2020, from the week when COVID-19-associated deaths reached their peak in Bavaria and Germany [23], as well as \(t_{ref}=31\) January 2022, as a more recent reference date when the prevalence of the Omicron sub-types first reached 99% of the evaluated samples in Germany [24], and compute the corresponding relative infections \(I_{rel}\)  
Figure 3: **Time series of infections and hospitalisation data. ****(a)** The grey line indicates the new infections, as reported by the RKI. The blue line indicates the 7-day moving average of the new infections. (**b)** The green line indicates the hospitalised COVID-19 patients in non-ICU on any given date, whereas the red line indicates the hospitalised COVID-19 patients in the ICU. For \(t_{ref}\) = 21 December 2020, the relative new infections \(I_{rel}(t,t_{ref})\) are mostly close to or lower than the new infections \(I_{D}(t)\), except for a short period in early 2020. Noticeably, from October 2021 onward, we observe that \(I_{rel}(t,t_{ref})\) is significantly lower than \(I_{D}(t)\). This implies that new infections \(I_{D}(t)\) from October 2021 onward overstate their additional burden to the hospital system in comparison to \(I_{D}(t_{ref})\). In contrast, for \(t_{ref}\) = 31 January 2022, the relative new infections \(I_{rel}(t,t_{ref})\) are significantly larger than the new infections \(I_{D}(t)\) over the whole course of the pandemic, except for time points close to and after \(t_{ref}\). This implies that the new infections \(I_{D}(t)\) over the course of the pandemic understate their additional burden on the healthcare system in comparison to \(I_{D}(t_{ref})\). The obvious main difference between the relative new infections \(I_{rel}(t,t_{ref})\) computed with respect to \(t_{ref}\) = 21 December 2020 and \(t_{ref}\) = 31 January 2022 is the order of magnitude of \(I_{rel}\). This can be explained by the difference in the hospitalisation rates at the two different reference dates: From 21 December 2020 to 31 January 2022, the estimate for \(k_{N}(t_{ref})\) decreased from 7.85% to 0.77%, i.e., by a factor of \(10.19\times\), while the estimate for \(k_{ICU}(t_{ref})\) decreased from 1.21% to 0.12%, i.e., by a factor of \(10.03\times\). Under the assumption of constant hospitalisation rates as on the reference date, the relative infections \(I_{rel}(t,t_{ref})\) are estimated such that the hospital beds model best explains the observed hospital bed occupancy. Hence, variations in the actual hospitalisation rates on different reference dates lead to similar variations in the computed relative infections \(I_{rel}\), as observed in Figure 5.  
For both cases, \(t_{ref}\) = 21 December 2020 and \(t_{ref}\) = 31 January 2022, six major peaks of the relative new infections \(I_{rel}(t,t_{ref})\) can be identified: April 2020, December 2020, April 2021, December 2021, March 2022, and October 2022.