## 2 Resilience-Based (RB) Methodology
This definition extended the original definition considerably by (1) considering resilience as a process, (2) introducing the psychological contribution and (3) referring to individuals. In the early 2000s, other definitions were proposed (such as [21, 22, 23]). These authors proposed an interrelated concept of resilience that considered technical, organizational, social and economic dimensions that could assess the performance of critical systems (i.e., electric power, water, road infrastructures and critical structures) and the social and economic dimensions of communities. The most comprehensive definition may be considered the one presented by UNISDR (2015) in the so-called Hyogo Framework, [24]. Resiliencewas defined as \"the capacity of a system, community or society potentially exposed to hazards to adapt, by resisting or changing in order to reach and maintain an acceptable level of functioning and structure. This is determined by the degree to which the social system is capable of organizing itself to increase this capacity for learning from past disasters for better future protection and to improve risk reduction measures.\" This modern definition took into account several contributions from previous works, in particularly, by underlining the importance of the social dimension and the role of learning from the past and future protection actions. [25; 26; 27] developed an analytical formulation to quantitatively calculate resilience by including recovery time (the period necessary to restore the functionality of the system to a desired level). In the structural arena, [28] proposed a formulation that quantified resilience by applying it to a series of hospital buildings. Several assumptions were made to establish the retrofit strategies: \"No Action\", \"Retrofit to life safety level\" and \"rebuild option\", corresponding to code levels: \"low\", \"intermediate\", \"high\", respectively. In particular, [28] investigated the case of earthquake scenarios, by considering four hazard levels and adapting earthquakes with 2%, 5% 10% and 20% probability of exceedance (PE) over 50 years. In the present paper, several hypotheses were considered. First, (1) the occupancy of intensity care units (ICU) was taken as the reference parameter for the assessment of losses. (2) The functionality was calculated as the percentage of the emptiness of the ICU, considered as the most representative parameter to model recovery. (3) Resilience was calculated in order to define the rapidity rate for the health infrastructure to recover to pre-event levels of functionality--thus facilitating discussions and considerations on the vulnerability of HSI. In particular, Figure 1 shows the national HSI capacities, in terms of ICU, before the COVID-19 crisis. The year inside the brackets indicates the latest data available [7] while EU14 means the mean values among the considered European Countries. It is worth noting that ICU capacity varied among the various countries due to several related parameters such as national policies, health infrastructural management and national economies. In particular, the mean value was 12.9 and, among the considered countries, two were above the mean (Germany and France at 33.9 and 16.3, respectively) and two were lower (United Kingdom and Italy at 10.5 and 8.6, respectively). The occupancy rates of ICUs during the months that followed the peak of the first wave were deduced from the databases that every country published in their respective official web sites. This paper proposed to consider the percentage of ICU capacity with respect to the peak value reached during the first wave of COVID-19. It is worth noting that these peaks  
Figure 1: Intensive care capacity—ICU beds before the COVID-19 crisis, latest year available (per 100,000 population) [7]. were not reached at the same time (even with small differences around the spring of 2020).