## 4 Discussion  
Figure 4 illustrates that both hospitalisation rates \(k_{N}(t)\) and \(k_{ICU}(t)\) changed significantly over the course of the pandemic. This makes it especially difficult to assess the severity of the pandemic situation based solely on the new infections \(I_{D}(t)\) alone, as the same number of new infections at different time points lead to significantly different constraints imposed on the hospital system. In particular, the impact of changing determinants of the pandemic (e.g., age structure of infected individuals, testing frequency, pre-existing immunity, viral variant) is implicitly reflected in the changes of the estimated hospitalisation rates. Moreover, the COVIX displays the same qualitative behaviour as the relative new infections, as all other things being equal, the COVIX increases (decreases) when daily new infections, hospitalisation rates, or both increase (decrease). Further, from a historic perspective, high COVIX values correspond to high observed hospital bed occupancy and therefore correctly identify periods of high added burden to the healthcare system due to COVID-19 patients. Hence, when continuously monitored over time, COVIX serves as an effective tool in assessing the severity of the pandemic. Although these are compelling strengths of COVIX, we would also like to discuss some weaknesses of our methodology. The intention of COVIX is to project changes in hospitalisation rates and new infections into a single severity index. On the one hand, this projection provides an unambiguous answer to when the pandemic situation improves or worsens--even when hospitalisation rates and new infections change in opposite directions. On the other hand, this dilutes granular information that could be extracted from tracking both of these metrics individually. Note, however, that analogous trade-offs need to be made by any such severity index with a similar objective. Furthermore, it is challenging to extrapolate the values of COVIX into the future. For a fixed reference date \(t_{ref}\), COVIX is  
Figure 6: **COVIX\((\mathbf{t},\mathbf{t}_{\text{ref}})\) with \(\mathbf{t}_{\text{ref}}\) = 21 December 2020**. The dashed red line indicates the chosen reference date. The multi-coloured line indicates the COVIX value at any given date. The colour of the line indicates whether the COVIX is above 60% (red), between 60% and 30% (yellow), or below 30% (green). proportional to the (relative) new infections \(I_{rel}(t,t_{ref})\) and therefore its forecasts encounter similar challenges as forecasts of new infections \(I_{D}(t)\) (see, e.g., [25; 26]). As suggested by the colour scheme in Figure 6, we propose to use the COVIX as an early-warning mechanism, which follows a traffic light system. Specifically, we propose the following approach:  
1. In collaboration with medical practitioners, epidemiologists, and public officials, identify a historic reference date \(t_{ref}\), which represents a threshold moment with respect to the dynamics and consequences of the pandemic that should not be overstepped (e.g., \(t_{ref}\) could correspond to a hospital overload). 2. In collaboration with medical practitioners, epidemiologists, and public officials, identify two additional reference dates \(t_{y}\) and \(t_{g}\), which define the following traffic lights at a given time \(t\):  
**Red--**COVIX(\(t,t_{ref}\)) \(>\) COVIDX(\(t_{y},t_{ref}\)):  
Major preventive measures have to be taken to prevent overstepping the severity at \(t_{ref}\). **Yellow--**COVIX(\(t_{y},t_{ref}\)) \(\geq\) COVIDX(\(t,t_{ref}\)) \(>\) COVIDX(\(t_{g},t_{ref}\)):  
All authors have read and agreed to the published version of the manuscript. Minor preventive measures have to be taken to prevent overstepping the severity at \(t_{ref}\). **Green--**COVIX(\(t_{g},t_{ref}\)) \(\geq\) COVIDX(\(t,t_{ref}\)):  
No preventive measures have to be taken to prevent overstepping the severity at \(t_{ref}\). 3. For each traffic light, define a set of measures to be taken, depending on the traffic light displayed by the COVIX. 4.