## 3 Defining and Quantifying the Degree of Emotional Concern
### Degree of Emotional Concern (\(\mathcal{C}\))  
Our special contribution in this work is to provide a method that defines an index to represent the population's concern, given that, to the best of our knowledge, no similar approaches have been made in the scientific community. The tools we use are mainly based on the information we have, that is, social interactions and Google searches for a series of terms.  
For this, we will use the Mood Variation \(\mathfrak{M}\) for the range of emotions centered around \"concern\", but also including close neighbors, such as \"preoccupied\", attempting to capture variations from similar mood, together with the Searching Behavior Index (\(SBI\)), a representative aggregation of the trends for the chosen searches. The degree of Emotional Concern \(\mathcal{C}\) can be therefore defined as:  
\[\mathcal{C}(L,\Delta t)\equiv\Phi(\mathfrak{M}_{m}(L,\Delta t),SBI(L,\Delta t)) \tag{15}\]  
where \(\Phi\) is a function that aggregates the normalized values of the Mood Variation and \(SBI\) by using ponderated weights, aiming to obtain a value representative of the results reflected by the emotional variation of the range of emotions close to concern, but also taking into account online searches as a contributing part where we include users who are  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Term** & **Valence** & **Arousal** & **Dominance** & **Term** & **Valence** & **Arousal** & **Dominance** \\ \hline alert & 5.38 & 5.14 & 6.58 & nervous & 3.56 & 5.51 & 4.02 \\ bored & 2.95 & 3.65 & 4.96 & relaxed & 7.25 & 2.49 & 7.09 \\ calm & 6.89 & 2.00 & 1.67 & sad & 2.10 & 3.49 & 3.84 \\ content & 6.70 & 3.17 & 5.92 & stress & 1.79 & 4.72 & 3.85 \\ depressed & 2.27 & 4.25 & 3.91 & serene & 4.67 & 1.48 & 6.50 \\ elated & 6.56 & 5.14 & 6.86 & tense & 2.75 & 5.32 & 4.72 \\ excited & 8.11 & 0.90 & 6.43 & upset & 2.45 & 4.49 & 4.30 \\ happy & 8.47 & 6.05 & 7.21 & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: VAD values for selected emotions [41].  
not active in Social Media and whose opinion could not, therefore, be collected or reflected on SMN at the time:  
\[\Phi(M,SBI)=\theta(L,t)\times\mathfrak{M}+(1-\theta(L,t))\times SBI \tag{16}\]  
In this equation, \(\theta\) is determined based on the location's Emotional Impact, compensating scenarios in which the Emotional Charge is closer to the neutral mood by giving more importance to the \(SBI\). This way, when Mood Variation is not enough due to a lower response in social interactions, we can compensate by increasing the contribution of the population's searching behavior. Firstly, we calculate the Mood Variation focused around the mood \"concerned\" for a time period \(\Delta t\) and a location \(L\). Once obtained, we normalize and re-scale the Mood Variation as well as the \(SBI\) in order to have a standardized measure. We aggregate these values as a weighted sum, resulting in the values comprising the degree of Emotional Concern for a period of time on a given location.  
In the subsequent sections, we are going to provide a description of the system we propose to build the method and implement these metrics, as well as discuss their performance with the help of a real-world example. The reader is going to get more clarity about the definition and the usage of the set of equations we just presented.