## 3 Results
### Correlation between Early Infected Rate and \(c^{*}\)/\(l^{*}\)  
We further investigated the correlation between a population actively engaged on social media with the outbreak of the infection. Specifically, we focused on the early stage of the COVID-19 outbreak in the 50 U.S. states, a period when the government had not yet started to take serious control measures. The infection rate in this stage is a reasonable proxy to measure the extent to which a state's residents rely on their individual awareness to protect themselves again the pandemic. Quantitively, we define the early infection rate as the proportion of residents being infected in the earliest \(T\) days since the state-level  
Figure 3: The distribution of \(c^{*}\) and \(l^{*}\) over 50 states for (**a**) Twitter and (**b–d**) Google Trends with different keywords.  
first case was confirmed (see the distribution of the early infection rate among 50 states in SI Figure S3).  
Having calculated both correlation strengths of Internet search and Twitter data and the early infection rate, we computed the relationship between the two. Surprisingly, we discovered a strong negative correlation between \(l^{*}\) and the early infection rate, with \(T\) varying from 1 week to 3 weeks, as shown in Table 2. This relationship indicates that the earlier people start tweeting and searching, the lower the infection rate. In other words, the earlier people tweeted about 'COVID-19' and searched for it on Google, the less people got infected when the virus breaks out. Moreover, we also find a significantly negative correlation between \(c^{*}\) and the infection rate using the Twitter data and Google Trends for the terms 'COVID' and 'COVID-19' on selected \(T\)'s (see Table 2), implying that the more predictive pro-active Internet-search behavior is, the lower the initial infected rate. Our assumption is that while each individual does not know that there will be a big outbreak, the aggregation of all people searching on Google or tweeting about COVID-19 indicates that there will be an outbreak. Note that we do not make a claim about causality. It could just be that becoming aware of COVID-19 increases the likelihood of a person experiencing flu-like symptoms getting tested for COVID-19, which means that more cases are detected. As the Wallstreet Journal reported (2019), more than 90 patients in central China were hospitalized with pneumonia or coronavirus-like symptoms in October and November 2019, indicating that COVID-19 might have spread before people became aware of it. Similarly, we are only claiming lagged correlation with detected COVID-19 cases and Twitter and Google search behavior. It could be that raising awareness will increase the likelihood of getting tested, thus driving up the incidence rate in the different states.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{\(c^{*}\)} \\ \hline  & **Twitter** & \begin{tabular}{c} **Google Trend** \\ **(coronavirus)** \\ \end{tabular} & \
\begin{tabular}{c} **Google Trend** \\ **(COVID)** \\ \end{tabular} &
\begin{tabular}{c} **Google Trend** \\ **(COVID-19)** \\ \end{tabular} \\ \hline Population size (2019) & 0.377 *** & 0.153 & 0.348 ** & 0.407 *** \\ \hline Population density (2019) & 0.381 *** & 0.268 * & 0.371 *** & 0.374 *** \\ \hline Enplanements (2018) & 0.230 * & 0.234 * & 0.389 *** & 0.419 *** \\ \hline Enplanements (2017) & 0.232 * & 0.237 * & 0.394 *** & 0.422 *** \\ \hline GDP (2019 Q4) & 0.413 *** & 0.184 & 0.382 *** & 0.435 *** \\ \hline GDP per capita (2019 Q4) & 0.208 & 0.418 *** & 0.504 *** & 0.403 *** \\ \hline \hline \end{tabular}
\end{table}
Table 1: The correlation coefficient between \(c^{*}\) and states’ variables in terms of population demographics, air traffic flow and the economic development level (\(n=50\)). The significance level is denoted by stars: * \(p<0.1\), ** \(p<0.05\), *** \(p<0.01\).