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Register a new userMulti-Stage Complex Contagions
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Added by
Sergey Melnik
Publication date
2011
fields
Informatics Engineering
and research's language is
English
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The spread of ideas across a social network can be studied using complex contagion models, in which agents are activated by contact with multiple activated neighbors. The investigation of complex contagions can provide crucial insights into social influence and behavior-adoption cascades on networks. In this paper, we introduce a model of a multi-stage complex contagion on networks. Agents at different stages --- which could, for example, represent differing levels of support for a social movement or differing levels of commitment to a certain product or idea --- exert different amounts of influence on their neighbors. We demonstrate that the presence of even one additional stage introduces novel dynamical behavior, including interplay between multiple cascades, that cannot occur in single-stage contagion models. We find that cascades --- and hence collective action --- can be driven not only by high-stage influencers but also by low-stage influencers.
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Since the publication of Complex Contagions and the Weakness of Long Ties in 2007, complex contagions have been studied across an enormous variety of social domains. In reviewing this decade of research, we discuss recent advancements in applied studies of complex contagions, particularly in the domains of health, innovation diffusion, social media, and politics. We also discuss how these empirical studies have spurred complementary advancements in the theoretical modeling of contagions, which concern the effects of network topology on diffusion, as well as the effects of individual-level attributes and thresholds. In synthesizing these developments, we suggest three main directions for future research. The first concerns the study of how multiple contagions interact within the same network and across networks, in what may be called an ecology of contagions. The second concerns the study of how the structure of thresholds and their behavioral consequences can vary by individual and social context. The third area concerns the roles of diversity and homophily in the dynamics of complex contagion, including both diversity of demographic profiles among local peers, and the broader notion of structural diversity within a network. Throughout this discussion, we make an effort to highlight the theoretical and empirical opportunities that lie ahead.
A major strategy to prevent the spread of COVID-19 is through the limiting of in-person contacts. However, for the many disabled people who live in the community and require caregivers to assist them with activities of daily living, limiting contacts is impractical or impossible. We seek to determine which interventions can prevent infections among disabled people and their caregivers. To accomplish this, we simulate COVID-19 transmission with a compartmental model on a network. The networks incorporate heterogeneity in the risks of different types of interactions, time-dependent lockdown and reopening measures, and interaction distributions for four different groups (caregivers, disabled people, essential workers, and the general population). Among these groups, we find the probability of becoming infected is highest for caregivers and second highest for disabled people. Our analysis of the network structure illustrates that caregivers have the largest modal eigenvector centrality among the four groups. We find that two interventions -- contact-limiting by all groups and mask-wearing by disabled people and caregivers -- particularly reduce cases among disabled people and caregivers. We also test which group most effectively spreads COVID-19 by seeding infections in a subset of each group and then comparing the total number of infections as the disease spreads. We find that caregivers are the most effective spreaders of COVID-19. We then test where limited vaccine doses could be used most effectively and we find that vaccinating caregivers better protects disabled people than vaccinating the general population, essential workers, or the disabled population itself. Our results highlight the potential effectiveness of mask-wearing, contact-limiting throughout society, and strategic vaccination for limiting the exposure of disabled people and their caregivers to COVID-19.
During the COVID-19 pandemic, conflicting opinions on physical distancing swept across social media, affecting both human behavior and the spread of COVID-19. Inspired by such phenomena, we construct a two-layer multiplex network for the coupled spread of a disease and conflicting opinions. We model each process as a contagion. On one layer, we consider the concurrent evolution of two opinions -- pro-physical-distancing and anti-physical-distancing -- that compete with each other and have mutual immunity to each other. The disease evolves on the other layer, and individuals are less likely (respectively, more likely) to become infected when they adopt the pro-physical-distancing (respectively, anti-physical-distancing) opinion. We develop approximations of mean-field type by generalizing monolayer pair approximations to multilayer networks; these approximations agree well with Monte Carlo simulations for a broad range of parameters and several network structures. Through numerical simulations, we illustrate the influence of opinion dynamics on the spread of the disease from complex interactions both between the two conflicting opinions and between the opinions and the disease. We find that lengthening the duration that individuals hold an opinion may help suppress disease transmission, and we demonstrate that increasing the cross-layer correlations or intra-layer correlations of node degrees may lead to fewer individuals becoming infected with the disease.
In social networks, interaction patterns typically change over time. We study opinion dynamics on tie-decay networks in which tie strength increases instantaneously when there is an interaction and decays exponentially between interactions. Specifically, we formulate continuous-time Laplacian dynamics and a discrete-time DeGroot model of opinion dynamics on these tie-decay networks, and we carry out numerical computations for the continuous-time Laplacian dynamics. We examine the speed of convergence by studying the spectral gaps of combinatorial Laplacian matrices of tie-decay networks. First, we compare the spectral gaps of the Laplacian matrices of tie-decay networks that we construct from empirical data with the spectral gaps for corresponding randomized and aggregate networks. We find that the spectral gaps for the empirical networks tend to be smaller than those for the randomized and aggregate networks. Second, we study the spectral gap as a function of the tie-decay rate and time. Intuitively, we expect small tie-decay rates to lead to fast convergence because the influence of each interaction between two nodes lasts longer for smaller decay rates. Moreover, as time progresses and more interactions occur, we expect eventual convergence. However, we demonstrate that the spectral gap need not decrease monotonically with respect to the decay rate or increase monotonically with respect to time. Our results highlight the importance of the interplay between the times that edges strengthen and decay in temporal networks.
In the study of infectious diseases on networks, researchers calculate epidemic thresholds to help forecast whether a disease will eventually infect a large fraction of a population. Because network structure typically changes in time, which fundamentally influences the dynamics of spreading processes on them and in turn affects epidemic thresholds for disease propagation, it is important to examine epidemic thresholds in temporal networks. Most existing studies of epidemic thresholds in temporal networks have focused on models in discrete time, but most real-world networked systems evolve continuously in time. In our work, we encode the continuous time-dependence of networks into the evaluation of the epidemic threshold of a susceptible--infected--susceptible (SIS) process by studying an SIS model on tie-decay networks. We derive the epidemic-threshold condition of this model, and we perform numerical experiments to verify it. We also examine how different factors---the decay coefficients of the tie strengths in a network, the frequency of interactions between nodes, and the sparsity of the underlying social network in which interactions occur---lead to decreases or increases of the critical values of the threshold and hence contribute to facilitating or impeding the spread of a disease. We thereby demonstrate how the features of tie-decay networks alter the outcome of disease spread.
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