Researchers from various scientific disciplines have attempted to forecast the spread of coronavirus disease 2019 (COVID-19). The proposed epidemic prediction methods range from basic curve fitting methods and traffic interaction models to machine-learning approaches. If we combine all these approaches, we obtain the Network Inference-based Prediction Algorithm (NIPA). In this paper, we analyse a diverse set of COVID-19 forecast algorithms, including several modifications of NIPA. Among the algorithms that we evaluated, the original NIPA performed best at forecasting the spread of COVID-19 in Hubei, China and in the Netherlands. In particular, we show that network-based forecasting is superior to any other forecasting algorithm.

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Designing an optimal network topology while balancing multiple, possibly conflicting objectives like cost, performance, and resiliency to viruses is a challenging endeavor, let alone in the case of decentralized network formation. We therefore propose a game-formation technique where each player aims to minimize its cost in installing links, the probability of being infected by a virus and the sum of hopcounts on its shortest paths to all other nodes.

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Spatially-close network fibers have a significant chance of failing simultaneously in the event of man-made or natural disasters within their geographic area. Network operators are interested in the proper detection and grouping of any existing spatially-close fiber segments, to avoid service disruptions due to simultaneous fiber failures. Moreover, spatially-close fibers can further be differentiated by computing the intervals over which they are spatially close. In this paper, we propose (1) polynomial-time algorithms for detecting all the spatially-close fiber segments of different fibers, (2) a polynomial-time algorithm for finding the spatially-close intervals of a fiber to a set of other fibers, and (3) a fast exact algorithm for grouping spatially-close fibers using the minimum number of distinct risk groups. All of our algorithms have a fast running time when simulated on three real-world network topologies.@en

Topological characteristics of links of complex networks influence the dynamical processes executed on networks triggered by links, such as cascading failures triggered by links in power grids and epidemic spread due to link infection. The line graph transforms links in the original graph into nodes. In this paper, we investigate how graph metrics in the original graph are mapped into those for its line graph. In particular, we study the degree distribution and the assortativity of a graph and its line graph. Specifically, we show, both analytically and numerically, the degree distribution of the line graph of an Erdős–Rényi graph follows the same distribution as its original graph. We derive a formula for the assortativity of line graphs and indicate that the assortativity of a line graph is not linearly related to its original graph. Additionally, line graphs of various graphs, e.g. Erdős–Rényi graphs, scale-free graphs, show positive assortativity. In contrast, we find certain types of trees and non-trees whose line graphs have negative assortativity.@en

Forming, in a decentralized fashion, an optimal network topology while balancing multiple, possibly conflicting objectives like cost, high performance, security and resiliency to viruses is a challenging endeavor. In this paper, we take a game-formation approach to network design where each player, for instance an autonomous system in the Internet, aims to collectively minimize the cost of installing links, of protecting against viruses, and of assuring connectivity. In the game, minimizing virus risk as well as connectivity costs results in sparse graphs. We show that the Nash Equilibria are trees that, according to the Price of Anarchy (PoA), are close to the global optimum, while the worst-case Nash Equilibrium and the global optimum may significantly differ for small infection rate and link installation cost. Moreover, the types of trees, in both the Nash Equilibria and the optimal solution, depend on the virus infection rate, which provides new insights into how viruses spread: for high infection rate τ, the path graph is the worst- and the star graph is the best-case Nash Equilibrium. However, for small and intermediate values of τ, trees different from the path and star graphs may be optimal.

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Shared effort games model people’s contribution to projects and sharing the obtained profits. Those games generalize both public projects like writing for Wikipedia, where everybody shares the resulting benefits, and all-pay auctions such as contests and political campaigns, where only the winner obtains a profit. In θ-equal sharing (effort) games, a threshold for effort defines which contributors win and then receive their (equal) share. (For public projects θ = 0 and for all-pay auctions θ = 1.) Thresholds between 0 and 1 can model games such as paper co-authorship and shared homework assignments. We study existence and efficiency of such games, to know what will happen in a given situation and where an intervention may be needed to improve the social welfare. First, we fully characterize the conditions for the existence of a pure-strategy Nash equilibrium for two-player shared effort games with close budgets and project value functions that are linear on the received contribution and prove some efficiency results. Second, since the theory does not work for more players, fictitious play simulations are used to show when such an equilibrium exists and what its efficiency is. The results about existence and efficiency of these equilibria provide the likely strategy profiles and the socially preferred strategies to use in real life situations of contribution to public projects.@en

Shared effort games model people's contribution to projects and sharing the obtained profits. Those games generalize both public projects like writing for Wikipedia, where everybody shares the resulting benefits, and all-pay auctions such as contests and political campaigns, where only the winner obtains a profit. In $ heta$-equal sharing (effort) games, a threshold for effort defines which contributors win and then receive their (equal) share. (For public projects $ heta = 0$ and for all-pay auctions $ heta = 1$.) Thresholds between 0 and 1 can model games such as paper co-authorship and shared homework assignments. First, we fully characterize the conditions for the existence of a pure-strategy Nash equilibrium for two-player shared effort games with close budgets and project value functions that are linear on the received contribution and prove some efficiency results. Second, since the theory does not work for more players, fictitious play simulations are used to show when such an equilibrium exists and what its efficiency is. The results about existence and efficiency of these equilibria provide the likely strategy profiles and the socially preferred strategies to use in real life situations of contribution to public projects. @en