## 3 Results
### The Variation of Correlation Strength over Time  
As the COVID-19 pandemic has been going on for many months, a lot has happened and changed. It is thus necessary to study the dynamic of the correlation between search and tweeting behavior and COVID-19 infections across time with extended data. Specifically, we further collected the state-level daily infection numbers, the COVID-keyword searches in Google Trends and the number of tweets in Twitter up until 30 September 2020. We find that the relationship between the COVID-19 pandemic spreading and the Internet data in all 50 U.S. states becomes weaker, especially in the last few months (see illustrations of four states in SI Figure S4). To further confirm the correlation variation over time, we calculate the optimal correlation strength \(c^{*}\) (the highest lagged Spearman correlation) on the different studied periods for the above-mentioned four states, as shown in Figure 4a-d. We can clearly see that \(c^{*}\) is almost always decreasing from spring to fall both for Google COVID-keyword searches and the number of tweets. Additionally, we carried out the same analysis for the remaining 46 states and found a similar reduction in \(c^{*}\), as shown in Supplementary Figure S5. In other words, the correlation of the COVID-keyword search and the number of tweets in the 50 U.S. states becomes weaker than at the beginning of the pandemic.  
These results show that the COVID-19 related terms and tweets cease correlating highly as time passes, which confirms previous research analyzing time-sensitive public events. For instance, Google's flu trends [17] or predicting U.S. elections ceased working well once people knew of its availability [18]. In the fall of 2020, COVID-19 had fully entered public awareness, and thus, people had no need to search for general information about this topic anymore. In other words, people were getting tired of terms such as 'COVID', and it just became part of daily life. As evidence, by collecting U.S. interest data on Google Trends (see Method for details), we found that the U.S. interest in searching 'coronavirus' peaked in the spring when the pandemic started to spread nationwide. After that, it was generally in line with daily search trends such as'music' or'sports' (see Figure 4e).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Early Infection Rate**} \\ \hline  & & **T = 7** & **T = 14** & **T = 21** \\ \hline  & Twitter & \(-0.358\) * & \(-0.439\) ** & \(-0.416\) ** \\ \cline{2-5}  & Google Trend & & & \\ (coronavirus) & \(-0.480\) *** & \(-0.570\) *** & \(-0.535\) *** \\ \cline{2-5} \(l^{*}\) & Google Trend & & & \\ (COVID) & \(-0.454\) *** & \(-0.544\) *** & \(-0.549\) *** \\ \cline{2-5}  & Google Trend & & & \\ (COVID-19) & \(-0.402\) *** & \(-0.488\) *** & \(-0.505\) *** \\ \hline  & Twitter & \(-0.442\) *** & \(-0.459\) *** & \(-0.377\) *** \\ \cline{2-5}  & Google Trend & & & \\ (coronavirus) & \(-0.100\) & \(-0.011\) & \(0.117\) \\ \cline{2-5} \(c^{*}\) & Google Trend & & & \\ (COVID) & \(-0.395\) ** & \(-0.346\) ** & \(-0.186\) \\ \cline{2-5}  & Google Trend & & & \\ (COVID-19) & \(-0.363\) *** & \(-0.289\) ** & \(-0.163\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The correlation coefficient between early infection rate for different T (number of days) and \(l^{*}\) and \(c^{*}\) from Internet data (\(n=50\)). Similar to Table 1, the stars represent the significance level, * \(p<0.1\), ** \(p<0.05\), *** \(p<0.01\).