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Early analyses revealed that dark web marketplaces (DWMs) started offering COVID-19 related products (e.g., masks and COVID-19 tests) as soon as the COVID-19 pandemic started, when these goods were in shortage in the traditional economy. Here, we broaden the scope and depth of previous investigations by considering how DWMs responded to an ongoing pandemic after the initial shock. Our dataset contains listings from 194 DWMs collected until July 2021. We start by focusing on vaccines. We find 248 listings offering approved vaccines, like Pfizer/BioNTech and AstraZeneca, as well as vendors offering fabricated proofs of vaccination and COVID-19 passports. Then, we consider COVID-19 related products. We show that, as the regular economy has become able to satisfy the demand of these goods, DWMs have decreased their offer. Next, we analyse the profile of vendors of COVID-19 related products and vaccines. We find that most of them are specialized in a single type of listings and are willing to ship worldwide. Finally, we consider a broader set of listings mentioning COVID-19, in order to assess the general impact of the pandemic on the broader activity of DWMs. Among 10,330 such listings, we show that recreational drugs are the most affected among traditional DWMs product, with COVID-19 mentions steadily increasing since March 2020. We anticipate that our results will be of interest to researchers, practitioners, and law enforcement agencies focused on the study and safeguard of public health. 

Abstract The COVID-19 pandemic has reshaped the demand for goods and services worldwide. The combination of a public health emergency, economic distress, and misinformation-driven panic have pushed customers and vendors towards the shadow economy. In particular, dark web marketplaces (DWMs), commercial websites accessible via free software, have gained significant popularity. Here, we analyse 851,199 listings extracted from 30 DWMs between January 1, 2020 and November 16, 2020. We identify 788 listings directly related to COVID-19 products and monitor the temporal evolution of product categories including Personal Protective Equipment (PPE), medicines (e.g., hydroxyclorochine), and medical frauds . Finally, we compare trends in their temporal evolution with variations in public attention, as measured by Twitter posts and Wikipedia page visits. We reveal how the online shadow economy has evolved during the COVID-19 pandemic and highlight the importance of a continuous monitoring of DWMs, especially now that real vaccines are available and in short supply. We anticipate our analysis will be of interest both to researchers and public agencies focused on the protection of public health. 

Abstract Worldwide urbanization calls for a deeper understanding of epidemic spreading within urban environments. Here, we tackle this problem through an agent-based model, in which agents move in a two-dimensional physical space and interact according to proximity criteria. The planar space comprises several locations, which represent bounded regions of the urban space. Based on empirical evidence, we consider locations of different density and place them in a core-periphery structure, with higher density in the central areas and lower density in the peripheral ones. Each agent is assigned to a base location, which represents where their home is. Through analytical tools and numerical techniques, we study the formation mechanism of the network of contacts, which is characterized by the emergence of heterogeneous interaction patterns. We put forward an extensive simulation campaign to analyze the onset and evolution of contagious diseases spreading in the urban environment. Interestingly, we find that, in the presence of a core-periphery structure, the diffusion of the disease is not affected by the time agents spend inside their base location before leaving it, but it is influenced by their motion outside their base location: a strong tendency to return to the base location favors the spreading of the disease. A simplified one-dimensional version of the model is examined to gain analytical insight into the spreading process and support our numerical findings. Finally, we investigate the effectiveness of vaccination campaigns, supporting the intuition that vaccination in central and dense areas should be prioritized. 

Filtering information in complex networks entails the process of removing interactions explained by a proper null hypothesis and retaining the remaining interactions, which form the backbone network. The reconstructed backbone network depends upon the accuracy and reliability of the available tools, which, in turn, are affected by the specific features of the available dataset. Here, we examine the performance of three approaches for the discovery of backbone networks, in the presence of heterogeneous, time-varying node properties. In addition to the recently proposed evolving activity driven model, we extend two existing approaches (the disparity filter and the temporal fitness model) to tackle time-varying phenomena. Our analysis focuses on the influence of the network size, which was previously shown to be a determining factor for the performance of the evolving activity driven model. Through mathematical and numerical analysis, we propose general guidelines for the use of these three approaches based on the available dataset. For small networks, the evolving temporal fitness model offers a more reasonable trade-off between the number of links assigned to the backbone network and the accuracy of their inference. The main limitation of this methodology lies in its computational cost, which becomes excessively high for large networks. In this case, the evolving activity driven model could be a valid substitute to the evolving temporal fitness model. If one seeks to minimize the number of links inaccurately included in the backbone network at the risk of dismissing many links that could belong to it, then the temporal disparity filter would be the approach-of-choice. Overall, our contribution expands the toolbox of network discovery in the technical literature and should help users in choosing the right network discovery instrument, depending on the problem considered.