# How Human Mobility Models Can Help to Deal with COVID-19
## 5 Evaluation of the Scenarios
### Physical Contacts Evaluation  
The characterisation of the exposure risk to the virus will depend mainly on the distance and duration of a physical contact between two individuals. Note that physical contacts are all possible contacts which can be obtained from the traces of the different scenarios. The procedure to obtain these physical contacts is based on iterating over the traces and determining every second which pairs of nodes are within a determined distance range. This allows us to obtain the total number of contacts and their duration, in addition to the individuals' location where the contact started. Thus, in order to study these physical contacts, we consider the following different distances: 2, 5, 10 m. For each scenario and distance, we obtained all the possible contacts and their durations. Note that most pairs of individuals, particularly in the synthetic generated scenarios, can contact at different times and with different durations, so we also consider the accumulated duration of these contacts. For example, three different contacts  
Figure 4: Density for m\({}^{2}\) of the synthetic scenarios. (**a**) Random WayPoint Model (RWP); (**b**) SWIM: (**c**) RWPa. Figure 5: Density for m\({}^{2}\) of the PedSim generated scenarios. (**a**) Plaza scenario. Note that the white rectangle in the centre corresponds to a fountain (nonwalkable); (**b**) Station scenario. between 2 individuals, with durations 2 s, 5 s, 1 s, results in an accumulated duration of 8 s. We use the accumulated duration since it reflects better the risk of exposure between a pair of individuals than considering only each contact separately. Thus, we obtain the following values:  
* C: Number of Contacts. The whole number of generated contacts. * P: Pairs Contacted. Number of different pairs of individuals that have contacted at least once. * P: Distribution of the accumulated duration of the contacts between pairs. * E[D]: Average accumulated duration obtained as the average of the previous distribution. In Table 2 we can see the number of contacts, pairs contacted and average contact time for the different scenarios and considering three distances. We also obtained the cumulative distribution function (CDF) of the accumulated contact duration \(P(X\leq T)\), as shown in Figure 6. Firstly, in Table 2 we can see the effect of social distancing on the PedSim generated mobility patterns: most of the contacts are greater than 2 m. Whereas in the Plaza scenario it was easy to keep this distance, the Station scenario evidences more difficulty for people keeping this distance, mainly when entering/exiting the train or passing through the turnstiles. As expected, there is a clear dependence between distance and duration: the longer the considered distance of a contact, the longer the average contact duration. The longer contact times are obtained in the synthetic scenarios (RWP, SWIM, RWPa), which is due mainly to the no renewal of individuals. Additionally, for the RWPa scenario, we can see the effect of the attraction points, which generates a huge amount of contacts around these points. These results are confirmed with the CDFs (Figure 6). RWP and SWIM scenarios are quite similar, showing a high percentage of low duration contacts. Nevertheless, for the RWPa scenario, we can see that for a distance of 10 m, practically all contacts are in the range of [150; 400] s.  
Figure 6: CDF of the contact durations for different distances in the following scenarios: (**a**) RWP; (**b**) SWIM; (**c**) RWPa; (**d**) Plaza; (**e**) Station. For the Plaza scenario, although the number of contacts is high, their duration is very short. This is due to the high renewal of individuals (note that every 60 s half of the individuals are renewed). Increasing the distance has little effect, as shown in the CDF in Figure 6d. Finally, for the Station scenario, we can find that the number of contacts is low although their duration is slightly longer.