## 2 Materials and Methods
### Dataset Description
This was translated into the following two conditions. First, we have wanted to investigate both on densely populated districts, like those comprised in the city of New York, and also in less populated areas. Second, we have also wanted to extend our analysis both to those counties that are comprised in NYC (or are very close to NYC), and to those counties that are further away from NYC. We decided to choose 12 different counties, that can be considered as clustered in three different groups. First, the counties/boroughs of NYC--New York (Manhattan), Kings (Brooklyn), Bronx (The Bronx), Richmond (Staten Island), and Queens (Queens). Second, the counties that are very/quite close to NYC--Nassau, Suffolk, Rockland, and Westchester. Third, a group of suburban, less populated counties that are far away from NYC--Onondaga, Oneida, and Monroe. Figure 1: PM2\({}_{2.5}\) and relative period (blue) vs. COVID-19 infections and relative period (red). The corresponding population density for each of the 12 counties is shown in the following Table 1, where the number of inhabitants is provided per square mile (1 square mile is equal to 2.58999 square kilometers), along with a total number of registered inhabitants, as per 2018 [30]. Before concluding this section, we need to return to the issue relative to the value of the PM\({}_{2.5}\) pollutant in the period under investigation (i.e., 19 February-8 March 2020). The first point to be considered is that the highest tolerable level of the PM\({}_{2.5}\) pollutant, indicated in the guidelines by the World Health Organization, is equal to 10 micrograms/m\({}^{3}\)[31]. In this regard, we should notice that in our period of interest (which is as long as 19 days), \begin{table}
\begin{tabular}{c c c} \hline \hline
**County** & **Density** & **Population** \\ \hline New York & 72,056 & 1,632,480 \\ Kings & 37,252 & 2,600,750 \\ Bronx & 21,132 & 1,437,870 \\ Queens & 34,194 & 2,298,510 \\ Richmond & 8149 & 474,101 \\ Nassau & 4763 & 1,356,560 \\ Westhester & 2250 & 968,815 \\ Rockland & 1866 & 323,686 \\ Suffolk & 1632 & 1,487,900 \\ Monroe & 1132 & 744,248 \\ Onondaga & 596 & 464,242 \\ Oneida & 190 & 230,782 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Population density of the twelve investigated counties. Figure 2: New York State map (studied counties: in grey). the number of times, when the PM\({}_{2.5}\) levels were above that threshold, were as many as 41, considering all the 12 counties. If we make a similar count for a longer time period, which extends from 19 February to the end of July (that is, a 168 days-long period), we yield a total number of PM\({}_{2.5}\) exceedances equal to 115. Even though we have already mentioned that the lockdown measures, adopted starting on 22 March, have probably altered the entire scenario (including the levels of pollution circulating in the air), it should be noted that our shorter period of interest had totaled the 35% of the total amount of PM\({}_{2.5}\) exceedances recorded in the longer period that extends from the beginning of the pandemic to its decay at the end of July 2020. Moreover, if we compare the average values of PM\({}_{2.5}\), measured in all the 12 counties in the two following different periods: 4-22 March vs. 19 February-end of July, we can notice an increase of the amount of PM\({}_{2.5}\) in the 4-22 March period, ranging from a minimum of almost +13% (New York) to a maximum of almost +50% (Oneida), with an average value of circa +24%, as calculated all over the 12 different counties. All these considerations are summarized in Table 2, where the values of the PM\({}_{2.5}\) particulate are given, as usual, in micrograms/m\({}^{3}\). In the second and third column, we show, respectively, the average values of PM\({}_{2.5}\), registered over the two different periods, while the aforementioned increase is given in the fourth and in the fifth column. The sixth and the seventh column account, instead, for the number of the PM\({}_{2.5}\) exceedances in the two periods. This was examined for all 12 counties.