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Register a new userThe role of directionality, heterogeneity and correlations in epidemic risk and spread
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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.
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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 contagion. In the population with only local random movement, whether the epidemic information is delayed or not has no effect on the spread of the epidemic. Peoples high sensitivity to the epidemic information leads to their risk aversion behavior and the spread of the epidemic is suppressed. In the population with only global person-to-person movement, timely and accurate epidemic information helps an individual cut off the connections with the infected in time and the epidemic is brought under control in no time. A delay in the epidemic information leads to an individuals misjudgment of who has been infected and who has not, which in turn leads to rapid progress and a higher peak of the epidemic. In the population with coexistence of local and global movement, timely and accurate epidemic information and peoples high sensitivity to the epidemic information play an important role in curbing the epidemic. A theoretical analysis indicates that peoples misjudgment caused by the delayed epidemic information leads to a higher encounter probability between the susceptible and the infected and peoples self-restricted travel behavior helps reduce such an encounter probability. A functional relation between the ratio of infected individuals and the susceptible-infected encounter probability has been found.
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 remains largely an open question, despite recent progresses in the case of static networks. Here, we consider as candidate structures the recently introduced concept of span-cores: the span-cores decompose a temporal network into subgraphs of controlled duration and increasing connectivity, generalizing the core-decomposition of static graphs. To assess the relevance of such structures, we explore the effectiveness of strategies aimed either at containing or maximizing the impact of a spread, based respectively on removing span-cores of high cohesiveness or duration to decrease the epidemic risk, or on seeding the process from such structures. The effectiveness of such strategies is assessed in a variety of empirical data sets and compared to baselines that use only static information on the centrality of nodes and static concepts of coreness, as well as to a baseline based on a temporal centrality measure. Our results show that the most stable and cohesive temporal cores play indeed an important role in epidemic processes on temporal networks, and that their nodes are likely to represent influential spreaders.
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. In this paper, we look at the system of two communities which are connected by bridge links between a fraction $r$ of bridge nodes, and study the effect of bridge nodes to the final state of the Susceptible-Infected-Recovered model, by mapping it to link percolation. By keeping a fixed average connectivity, but allowing different transmissibilities along internal and bridge links, we theoretically derive different power-law asymptotic behaviors of the total fraction of the recovered $R$ in the final state as $r$ goes to zero, for different combinations of internal and bridge link transmissibilities. We also find crossover points where $R$ follows different power-law behaviors with $r$ on both sides when the internal transmissibility is below but close to its critical value, for different bridge link transmissibilities. All of these power-law behaviors can be explained through different mechanisms of how finite clusters in each community are connected into the giant component of the whole system, and enable us to pick effective epidemic strategies and to better predict their impacts.
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 studies and policies simply constrain the distance r individuals may travel from their home or neighbourhood. However, the epidemic risk is related not only to distance travelled, but also to frequency of contacts, which is proxied by the frequency f with which individuals revisit locations over a given reference period. Inspired by recent literature that uncovers a clear universality pattern on how r and f interact in routine human mobility, this paper addresses the following question: does this universal relation between r and f carry over to epidemic spreading, so that the risk associated with human movement can be modeled by a single, unifying variable r * f? To answer this question, we use two large-scale datasets of individual human mobility to simulate disease spread. Results show that a universal relation between r and f indeed exists in the context of epidemic spread: in both of the datasets, the final size and the spatial distribution of the infected population depends on the product r * f more directly than on the individual values of r and f. The important implication here is that restricting r (where you can go), but not f (how frequently), could be unproductive: high frequency trips to nearby locations can be as dangerous for disease spread as low frequency trips to distant locations. This counter-intuitive discovery could explain the modest effectiveness of distance-based travel restrictions and could inform future policies on COVID-19 and other epidemics.
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 activities obtained from digital trace data. In this study, the Venables distance (D_v), and the activity density (D_a) are used to quantify and evaluate human activities for 193 US counties, whose cumulative number of confirmed cases was greater than 100 as of March 31, 2020. Venables distance provides a measure of the agglomeration of the level of human activities based on the average distance of human activities across a city or a county (less distance could lead to a greater contact risk). Activity density provides a measure of level of overall activity level in a county or a city (more activity could lead to a greater risk). Accordingly, Pearson correlation analysis is used to examine the relationship between the two human activity indicators and the basic reproduction number in the following weeks. The results show statistically significant correlations between the indicators of human activities and the basic reproduction number in all counties, as well as a significant leader-follower relationship (time lag) between them. The results also show one to two weeks lag between the change in activity indicators and the decrease in the basic reproduction number. This result implies that the human activity indicators provide effective early indicators for the spread risk of the pandemic during the early stages of the outbreak. Hence, the results could be used by the authorities to proactively assess the risk of disease spread by monitoring the daily Venables distance and activity density in a proactive manner.
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