# The Assessment of COVID-19 Vulnerability Risk for Crisis Management
## 2 Materials and Methods
#### Criteria and Weights  
Based on the literature review it was assumed that the criteria needed to determine the CVI were basic country demographic statistics listed in Table 1.  
This simple set of criteria enables the implementation of the COVID-19 vulnerability risk assessment algorithm by all, even less advanced countries if needed. The research was based on several open data sources, such as web services that present demographic statistics: destatis.de [91] and the Robert Koch Institute Site [92], were used. Furthermore, to estimate the information on the transport network, selected data from OpenStreetMap were acquired and analysed. [93]. The case study area was limited to Germany, and the analyses were divided by regions. The listed criteria presented in Table 1 can be grouped into two categories: dynamic (quickly changing in time) and static (slowly changing in time or static). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Criteria** & **Criteria Explanation** & **Data Source** & **Criteria Type** \\ \hline Cas & Number of COVID cases per 100,000 inhabitants & rki.de & \\ Serv & Turnover rate for accommodation and food services in relation & & \\  & to the period before the pandemic & & \\ Mb & The estimation of population movement & destatis.de & \\ Hsp & Number of COVID hospitalisations per 100,000 inhabitants & rki.de & \\ Vacc & Population percentage of two doses vaccinated & rki.de & \\ \hline Hos & Number of hospitals in the region per 100,000 inhabitants & destatis.de & \\ Hbed & Total number of hospital beds on region per 100,000 inhabitants & destatis.de & \\ PDen & Population density per sq. km & destatis.de & \\ Rd & Total length of roads in the region & OSM & \\ Rs & Total length of railways in the region & OSM & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: SMCA criteria and criteria data sources (own study). The criteria determination process was followed by the pairwise comparison that resulted in the importance determination (in accordance with the AHP methodology). The importance of relations can be found in Table 2. The larger the relative importance values were, the stronger the relation that can be assigned to the pair of criteria. The methodology was used to select and compare the criteria. Pairwise comparisons resulted in the estimation of weights that are presented in Table 3. Validation of calculated weights returns Consistency Ratio (CR), which was 0.10; Consistency Index (CI) 0.15. According to the weights listed in the table, the greatest importance can be assigned to the following criteria: Hos, Hbed, Cas, PDen, Hsp. Analysis of results in the static and dynamic groups show that the static criteria affected the CVI estimation twice as strongly as the dynamic criteria (static sum weights: 0.66; dynamic sum weights: 0.34). To calculate the CVI of the region, the criteria vulnerability score was determined based on the categories in Table 4 (the remaining criteria risk score available in Appendix A). The assigned vulnerability score (VSc) takes values in the range from 2 to 8. The high score represents a high vulnerability in the term of the relevant criterion. For example, density--greater than 2000 people per sq. km--corresponds to the vulnerability value of 8. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Criteria/VSc** & **PDen** & **Serv** & **Hos** & **Hbed** & **Cas** & **Vacc** \\ \hline
2 & \(<\)100 & \(<\)20 & \(>\)10 & \(>\)2000 & \(<\)1 & \(>\)75 \\
3 & 100–200 & 20–40 & 8–10 & 1400–2000 & 1–2 & 60–75 \\
4 & 200–300 & 40–55 & 6–8 & 800–1400 & 2–6 & 50–60 \\
5 & 300–500 & 55–70 & 4–6 & 400–800 & 6–12 & 30–50 \\
6 & 500–1000 & 70–85 & 2–4 & 200–400 & 12–20 & 15–30 \\
7 & 1000–2000 & 85–100 & 1–2 & 100–200 & 20–30 & 5–15 \\
8 & \(>\)2000 & \(>\)100 & \(<\)1 & \(<\)100 & \(>\)30 & \(<\)5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The selected criteria scores (own study based on [90]).