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Most models of epidemic spread, including many designed specifically for COVID-19, implicitly assume that social networks are undirected, i.e., that the infection is equally likely to spread in either direction whenever a contact occurs. In particular, this assumption implies that the individuals most likely to spread the disease are also the most likely to receive it from others. Here, we review results from the theory of random directed graphs which show that many important quantities, including the reproductive number and the epidemic size, depend sensitively on the joint distribution of in- and out-degrees (risk and spread), including their heterogeneity and the correlation between them. By considering joint distributions of various kinds we elucidate why some types of heterogeneity cause a deviation from the standard Kermack-McKendrick analysis of SIR models, i.e., so called mass-action models where contacts are homogeneous and random, and some do not. We also show that some structured SIR models informed by complex contact patterns among types of individuals (age or activity) are simply mixtures of Poisson processes and tend not to deviate significantly from the simplest mass-action model. Finally, we point out some possible policy implications of this directed structure, both for contact tracing strategy and for interventions designed to prevent superspreading events. In particular, directed networks have a forward and backward version of the classic friendship paradox -- forward links tend to lead to individuals with high risk, while backward links lead to individuals with high spread -- such that a combination of both forward and backward contact tracing is necessary to find superspreading events and prevent future cascades of infection.
By incorporating delayed epidemic information and self-restricted travel behavior into the SIS model, we have investigated the coupled effects of timely and accurate epidemic information and peoples sensitivity to the epidemic information on contagio
Temporal networks are widely used to represent a vast diversity of systems, including in particular social interactions, and the spreading processes unfolding on top of them. The identification of structures playing important roles in such processes
Power-law behaviors are common in many disciplines, especially in network science. Real-world networks, like disease spreading among people, are more likely to be interconnected communities, and show richer power-law behaviors than isolated networks.
Travel restrictions have often been used as a measure to combat the spread of disease -- in particular, they have been extensively applied in 2020 against coronavirus disease 2019 (COVID-19). How to best restrict travel, however, is unclear. Most stu
The spread of pandemics such as COVID-19 is strongly linked to human activities. The objective of this paper is to specify and examine early indicators of disease spread risk in cities during the initial stages of outbreak based on patterns of human