# How Human Mobility Models Can Help to Deal with COVID-19
## 6 Analysis of COVID-19 Transmission
### Exposure Risk Characterisation  
Based on the previous studies, in this subsection, we propose two alternative methods to obtain the exposure risk. The first one is based on obtaining the risky contacts, that is, the contacts which can be susceptible to transmit the disease. The second method is based on Expression (3), which is a more generic expression of the exposure risk considering also the impact of the environment.  
According to the European Centre for Disease Prevention and Control (ECDC) [70], a contact is classified with high-risk exposure if a person has had face-to-face contact with a COVID-19 case within 2 m for more than 15 min (900 s). The USA's CDC (Centers for Disease Control and Prevention) [71] also has a similar definition: an individual who has had close contact (less than 6 feet \(\approx\) 1.83 m ) for 15 or more min. Following these strict criteria, no contact in the generated scenarios would be considered a high-risk exposure, since for 2 m the maximum contact duration is 500 s (less than 8 min), as can be seen in Figure 6.  
Nevertheless, recent studies [9; 72] have shown that all exposure time counts and even the CDC has revised its guidance, acknowledging that even brief contacts can lead to transmission. So, a more useful approach is to measure the number of minutes exposed to risky contacts. This is the last method used by the smartphone-based contact tracing apps using the Application Program Interface (API) jointly developed by Apple and Google. Apple has defined an Exposure Risk Value (ERV) to allow health authorities to define when to alert a user that they may have been exposed to someone diagnosed with COVID-19 which is measured in Meaningful Exposure Minutes (MEMs) units [73]. Although ERV offers flexibility in calculating this value by setting weights and values related to bluetooth attenuations, the infectiousness of the affected individual and diagnosis report type, in this paper we will obtain only the minutes exposed to a contact. For example, an ERV of 10 MEMs reflects that an individual has been exposed to risk contacts for an accumulated time of 10 min.  
Nevertheless, the ERV only takes into account the (discretised) distance and time of the contacts, omitting the impact of the environment. Thus, based on the previous study of Section 6.1 we propose the following expression, Exposure Risk with Quality (ERQ), which is not only based on the (continuous) distance and time between individuals but also on the quality of the medium:  
\[ERQ=K\cdot Q_{m}\frac{t}{\max(d,0.3)^{2}} \tag{4}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Quality of the Medium** & **Good** & **Moderate** & **Bad** \\ \hline Air renewal & 1 & 2/3 & 1/3 \\ Temperature & 1 & 2/3 & 1/3 \\ Solar radiation & 1 & 2/3 & 1/3 \\ \hline Value & 1 & 2/3 & 1/3 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Quality of the medium. Assignment of values. Good stands for good quality of virus transmission and it means no air renewal, low temperature, and no solar radiation.  
This expression is a slight adaption of Expression (3). The risk is inversely proportional to the square of the distance, so for long distances, the exposure risk will be practically negligible. On the contrary, for very close encounters the risk will increase exponentially, up to 0.3 m, which is the minimum interpersonal distance [74]. Note that this limit also avoids a singularity at \(d=0\).  
In order to normalise this expression, we use the same units (MEMs) than in the previous ERV expression. For obtaining the value of \(K\) in expression, we consider that one minute of MEMs is equivalent to a contact with a duration of one minute and within a distance of one metre (the average distance used in the ERV), considering also an average quality of the medium (\(Q_{m}=0.5\)). Therefore, if \(t\) is expressed in minutes and \(d\) in metres, and working out the value of \(K\) in Expression (4) we obtain a value of \(1/30\) m\({}^{2}\).