# COVID-19's Impact on International Trade
###### Abstract
The further development of Google matrix applications to the WTN allowed researchers to perform the analysis of the multiproduct WTN [26] by considering the contributions of the products proportionally to their trade volumes and treating countries on equal grounds, which corresponds to the fundamental principle of the UN. These methods were also successfully applied to the networks of economic activities provided by the WTO [27]. In addition, the reduced Google matrix (REGOMAX) algorithm has been applied to the multiproduct WTN [28] and to the multisectorial trade network [29]. This algorithm has been developed and numerically tested in [30; 31; 32]. For a subset of interest, constituted by a moderate number \(N_{r}\) of network nodes, this algorithm finds the effective interactions between these \begin{table}
\begin{tabular}{c l} \hline \hline
**SITC Code** & **Standard International Trade Classification (SITC) Product Groups** \\ \hline
0 & Food and live animals \\
1 & Beverages and tobacco \\
2 & Crude materials, inedible, except fuels \\
3 & Mineral fuels, lubricants and related materials \\
4 & Animal and vegetable oils, fats and waxes \\
5 & Chemicals and related products, n.e.s. \\
6 & Manufactured goods classified chiefly by material \\
7 & Machinery and transport equipment \\
8 & Miscellaneous manufactured articles \\
9 & Commodities and transactions not classified elsewhere in the SITC \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of product groups from the Standard International Trade Classification (SITC) [13]. \(N_{r}\) nodes taking into account all the indirect pathways passing through the global network of a much larger size \(N\gg N_{r}\). For the here-studied WTN case, the size of the global network is \(N=N_{c}N_{p}=194\times 10=1940\). Using the above-cited algorithms, we analyze here the impact of COVID-19 on the WTN for the years 2018-2020. In the last couple of years, there has been a growing interest in the network analysis of the influence of COVID-19 on international trade (see e.g., [33; 34; 35; 36]). All of these previous works, usually based on standard centrality measures such as the node degree or betweenness centralities, only consider the import flows network. However, the import flows network and export flows network, which are structurally different, are equally important; e.g., the study [33] was focused on the analysis of the PageRank (analogous to the ImportRank), while the CheiRank (analogous to the ExportRank) was not considered. The above-cited previous works consider either the global trade network constructed by summing or averaging the economic flows between each pair of countries or a specific economical sector; e.g., the cereal trade in [35]. Here, in the present work, we take into account the trade of all commodities, gathered into the 10 product groups of the Standard International Trade Classification (SITC) (see Table 1). The constructed multiproduct WTN allows us to take account of the relative economical importance of each product. In addition, many of the previous works focused their analysis on the trade between either a dozen economically leading countries or a specific set of countries; e.g., in [34] with the Association of Southeast Asian Nations (ASEAN) countries. Here, we consider the trade transactions yearly reported in the UN Comtrade database of all the commodities between 194 countries and territories. The new advantage of our approach is due to the Google matrix analysis of the WTN [18; 25; 26; 27; 28; 29], which allows us to treat multiproduct commercial trade flows between world countries, taking account of ingoing and outgoing flow directions and considering all the countries on equal grounds independent of their wealth. The REGOMAX method developed in [28; 30; 31] allows us to highlight interdependencies between specific products and countries. For all these reasons, our global Google matrix analysis, including the REGOMAX algorithm, allows us to obtain a much deeper characterization of the impact of COVID-19 on the WTN.