Physical contacts result in the spread of various phenomena such as viruses, gossips, ideas, packages and marketing pamphlets across a population. The spread depends on how people move and co-locate with each other, or their mobility patterns. How far such phenomena spread has significance for both policy making and personal decision making, e.g., studying the spread of COVID-19 under different intervention strategies such as wearing a mask. In practice, mobility patterns of an entire population is never available, and we usually have access to location data of a subset of individuals. In this paper, we formalize and study the problem of estimating the spread of a phenomena in a population, given that we only have access to sub-samples of location visits of some individuals in the population. We show that simple solutions such as estimating the spread in the sub-sample and scaling it to the population, or more sophisticated solutions that rely on modeling location visits of individuals do not perform well in practice, the former because it ignores contacts between unobserved individuals and sampled ones and the latter because it yields inaccurate modeling of co-locations. Instead, we directly model the co-locations between the individuals. We introduce PollSpreader and PollSusceptible, two novel approaches that model the co-locations between individuals using a contact network, and infer the properties of the contact network using the subsample to estimate the spread of the phenomena in the entire population. We show that our estimates provide an upper bound and a lower bound on the spread of the disease in expectation. Finally, using a large high-resolution real-world mobility dataset, we experimentally show that our estimates are accurate, while other methods that do not correctly account for co-locations between individuals result in wrong observations (e.g, premature herd-immunity).
In this paper, we study the spreading speed of complex contagions in a social network. A $k$-complex contagion starts from a set of initially infected seeds such that any node with at least $k$ infected neighbors gets infected. Simple contagions, i.e., $k=1$, quickly spread to the entire network in small world graphs. However, fast spreading of complex contagions appears to be less likely and more delicate; the successful cases depend crucially on the network structure~\cite{G08,Ghasemiesfeh:2013:CCW}. Our main result shows that complex contagions can spread fast in a general family of time-ev…
Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth's surface; however, in modern contagions long-range edges -- for example, due to airline transportation or communication media -- allow clusters of a contagion to appear in distant locations. Here we study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct "contagion maps" that use multiple contagions on a network to map the nodes as a point cl…
Prior social contagion models consider the spread of either one contagion at a time on interdependent networks or multiple contagions on single layer networks or under assumptions of competition. We propose a new threshold model for the diffusion of multiple contagions. Individuals are placed on a multiplex network with a periodic lattice and a random-regular-graph layer. On these population structures, we study the interface between two key aspects of the diffusion process: the level of synergy between two contagions, and the rate at which individuals become dormant after adoption. Dormancy i…
Social contagion is the process in which people adopt a belief, idea, or practice from a neighbor and pass it along to someone else. For over 100 years, scholars of social contagion have almost exclusively made the same implicit assumption: that only one belief, idea, or practice spreads through the population at a time. It is a default assumption that we don't bother to state, let alone justify. The assumption is so ingrained that our literature doesn't even have a word for "whatever is to be diffused", because we have never needed to discuss more than one of them. But this assumption is obvi…
It is commonly believed that information spreads between individuals like a pathogen, with each exposure by an informed friend potentially resulting in a naive individual becoming infected. However, empirical studies of social media suggest that individual response to repeated exposure to information is significantly more complex than the prediction of the pathogen model. As a proxy for intervention experiments, we compare user responses to multiple exposures on two different social media sites, Twitter and Digg. We show that the position of the exposing messages on the user-interface strongly…
Increasing evidence suggests that, similar to face-to-face communications, human emotions also spread in online social media. However, the mechanisms underlying this emotional contagion, for example, whether different feelings spread in unlikely ways or how the spread of emotions relates to the social network, is rarely investigated. Indeed, because of high costs and spatio-temporal limitations, explorations of this topic are challenging using conventional questionnaires or controlled experiments. Because they are collection points for natural affective responses of massive individuals, online…
Increasing levels of far-right extremist violence have generated public concern about the spread of radicalization in the United States. Previous research suggests that radicalized individuals are destabilized by various environmental (or endemic) factors, exposed to extremist ideology, and subsequently reinforced by members of their community. As such, the spread of radicalization may proceed through a social contagion process, in which extremist ideologies behave like complex contagions that require multiple exposures for adoption. In this study, I applied an epidemiological method called tw…
An outstanding problem of interdisciplinary interest is to understand quantitatively the role of social contacts in contagion dynamics. In general, there are two types of contacts: close ones among friends, colleagues and family members, etc., and ordinary contacts from encounters with strangers. Typically, social reinforcement occurs for close contacts. Taking into account both types of contacts, we develop a contact-based model for social contagion. We find that, associated with the spreading dynamics, for random networks there is coexistence of continuous and discontinuous phase transitions…
The spread of socially-learnt behaviours occurs in many animal species, and understanding how behaviours spread can provide novel insights into the causes and consequences of sociality. Within wild populations, behaviour spread is often assumed to occur as a "simple contagion". Yet, emerging evidence suggests behaviours may frequently spread as "complex contagions", and this holds significant ramifications for the modes and extent of transmission. We present a new framework enabling comprehensive examination of behavioural contagions by integrating social-learning strategies into network-based…
Social network analysis is now widely used to investigate the dynamics of infectious disease spread from person to person. Vaccination dramatically disrupts the disease transmission process on a contact network, and indeed, sufficiently high vaccination rates can disrupt the process to such an extent that disease transmission on the network is effectively halted. Here, we build on mounting evidence that health behaviors - such as vaccination, and refusal thereof - can spread through social networks through a process of complex contagion that requires social reinforcement. Using network simulat…
The threshold model is a simple but classic model of contagion spreading in complex social systems. To capture the complex nature of social influencing we investigate numerically and analytically the transition in the behavior of threshold-limited cascades in the presence of multiple initiators as the distribution of thresholds is varied between the two extreme cases of identical thresholds and a uniform distribution. We accomplish this by employing a truncated normal distribution of the nodes' thresholds and observe a non-monotonic change in the cascade size as we vary the standard deviation.…
Complex contagions describe diffusion of behaviors in a social network in settings where spreading requires the influence by two or more neighbors. In a $k$-complex contagion, a cluster of nodes are initially infected, and additional nodes become infected in the next round if they have at least $k$ already infected neighbors. It has been argued that complex contagions better model behavioral changes such as adoption of new beliefs, fashion trends or expensive technology innovations. This has motivated rigorous understanding of spreading of complex contagions in social networks. Despite simple …
Most studies on social influence have focused on direct influence, while another interesting question can be raised as whether indirect influence exists between two users who're not directly connected in the network and what affects such influence. In addition, the theory of \emph{complex contagion} tells us that more spreaders will enhance the indirect influence between two users. Our observation of intensity of indirect influence, propagated by $n$ parallel spreaders and quantified by retweeting probability on Twitter, shows that complex contagion is validated globally but is violated locall…
Contact tracing can be thought of as a race between two processes: an infection process and a tracing process. In this paper, we study a simple model of infection spreading on a tree, and a tracer who stabilizes one node at a time. We focus on the question, how should the tracer choose nodes to stabilize so as to prevent the infection from spreading further? We study simple policies, which prioritize nodes based on time, infectiousness, or probability of generating new contacts.
We complement the rich conceptual work on organizational corruption by quantitatively modelling the spread of corruption within organizations. We systematically vary four organizational culture-related parameters, i.e., organization structure, location of bad apple, employees propensity to become corrupted (corruption probability), and number of whistle-blowers. Our simulation studies find that in organizations with flatter structures, corruption permeates the organization at a lower threshold value of corruption probability compared to those with taller structures. However, the final proporti…
The temporal dynamics of social interactions were shown to influence the spread of disease. Here, we model the conditions of progression and competition for several viral strains, exploring various levels of cross-immunity over temporal networks. We use our interaction-driven contagion model and characterize, using it, several viral variants. Our results, obtained on temporal random networks and on real-world interaction data, demonstrate that temporal dynamics are crucial to determining the competition results. We consider two and three competing pathogens and show the conditions under which …
Heterogeneous adoption thresholds exist widely in social contagions, but were always neglected in previous studies. We first propose a non-Markovian spreading threshold model with general adoption threshold distribution. In order to understand the effects of heterogeneous adoption thresholds quantitatively, an edge-based compartmental theory is developed for the proposed model. We use a binary spreading threshold model as a specific example, in which some individuals have a low adoption threshold (i.e., activists) while the remaining ones hold a relatively high adoption threshold (i.e., bigots…
How does network structure affect diffusion? Recent studies suggest that the answer depends on the type of contagion. Complex contagions, unlike infectious diseases (simple contagions), are affected by social reinforcement and homophily. Hence, the spread within highly clustered communities is enhanced, while diffusion across communities is hampered. A common hypothesis is that memes and behaviors are complex contagions. We show that, while most memes indeed behave like complex contagions, a few viral memes spread across many communities, like diseases. We demonstrate that the future popularit…
We present a computational approach for estimating emotion contagion on social media networks. Built on a foundation of psychology literature, our approach estimates the degree to which the perceivers' emotional states (positive or negative) start to match those of the expressors, based on the latter's content. We use a combination of deep learning and social network analysis to model emotion contagion as a diffusion process in dynamic social network graphs, taking into consideration key aspects like causality, homophily, and interference. We evaluate our approach on user behavior data obtaine…
Adoption of innovations, products or online services is commonly interpreted as a spreading process driven to large extent by social influence and conditioned by the needs and capacities of individuals. To model this process one usually introduces behavioural threshold mechanisms, which can give rise to the evolution of global cascades if the system satisfies a set of conditions. However, these models do not address temporal aspects of the emerging cascades, which in real systems may evolve through various pathways ranging from slow to rapid patterns. Here we fill this gap through the analysis…
Social networks have emerged as a critical factor in information dissemination, search, marketing, expertise and influence discovery, and potentially an important tool for mobilizing people. Social media has made social networks ubiquitous, and also given researchers access to massive quantities of data for empirical analysis. These data sets offer a rich source of evidence for studying dynamics of individual and group behavior, the structure of networks and global patterns of the flow of information on them. However, in most previous studies, the structure of the underlying networks was not d…
When an infection spreads in a community, an individual's probability of becoming infected depends on both her susceptibility and exposure to the contagion through contact with others. While one often has knowledge regarding an individual's susceptibility, in many cases, whether or not an individual's contacts are contagious is unknown. We study the problem of predicting if an individual will adopt a contagion in the presence of multiple modes of infection (exposure/susceptibility) and latent neighbor influence. We present a generative probabilistic model and a variational inference method to …
Security games model the confrontation between a defender protecting a set of targets and an attacker who tries to capture them. A variant of these games assumes security interdependence between targets, facilitating contagion of an attack. So far only stochastic spread of an attack has been considered. In this work, we introduce a version of security games, where the attacker strategically drives the entire spread of attack and where interconnections between nodes affect their susceptibility to be captured. We find that the strategies effective in the settings without contagion or with stocha…
We investigate opinion spreading by a threshold model in a situation where the influence of people is heterogeneously distributed. We focus on the response of the average opinion as a function between the trend between out-degree (number of neighbors)---effectively the strength of influence of a node---and the threshold for adopting a new product or opinion. We find that if the coupling is very positive, the final state of the system will be a mix of different opinions otherwise it will it converges to a consensus state. We find that this cannot be simply explained as a phase transition, but e…
We develop a theoretical framework for the study of epidemic-like social contagion in large scale social systems. We consider the most general setting in which different communication platforms or categories form multiplex networks. Specifically, we propose a contact-based information spreading model, and show that the critical point of the multiplex system associated to the active phase is determined by the layer whose contact probability matrix has the largest eigenvalue. The framework is applied to a number of different situations, including a real multiplex system. Finally, we also show th…
Increasing evidence suggests that, similar to face-to-face communications, human emotions also spread in online social media. However, the mechanisms underlying this emotion contagion, for example, whether different feelings spread in unlikely ways or how the spread of emotions relates to the social network, is rarely investigated. Indeed, because of high costs and spatio-temporal limitations, explorations of this topic are challenging using conventional questionnaires or controlled experiments. Because they are collection points for natural affective responses of massive individuals, online s…
The graph invariant examined in this paper is the largest eigenvalue of the adjacency matrix of a graph. Previous work demonstrates the tight relationship between this invariant, the birth and death rate of a contagion spreading on the graph, and the trajectory of the contagion over time. We begin by conducting a simulation confirming this and explore bounds on the birth and death rate in terms of well-known graph invariants. As a result, the change in the largest eigenvalue resulting from removal of a vertex in the network is the best measure of effectiveness of interventions that slow the sp…
Contacts' temporal ordering and dynamics are crucial for understanding the transmission of infectious diseases. We introduce an interaction-driven model of an airborne disease over contact networks. We demonstrate our interaction-driven contagion model, instantiated for COVID-19, over history-maintaining random temporal networks and real-world contacts. We use it to evaluate temporal, spatiotemporal, and spatial social distancing policies. We find that a spatial distancing policy is mainly beneficial at the early stages of a disease. We then continue to evaluate temporal social distancing, tha…
Network epidemiology has become a vital tool in understanding the effects of high-degree vertices, geographic and demographic communities, and other inhomogeneities in social structure on the spread of disease. However, many networks derived from modern datasets are quite dense, such as mobility networks where each location has links to a large number of potential destinations. One way to reduce the computational effort of simulating epidemics on these networks is sparsification, where we select a representative subset of edges based on some measure of their importance. Recently an approach wa…
Contagious processes, such as spread of infectious diseases, social behaviors, or computer viruses, affect biological, social, and technological systems. Epidemic models for large populations and finite populations on networks have been used to understand and control both transient and steady-state behaviors. Typically it is assumed that after recovery from an infection, every agent will either return to its original susceptible state or acquire full immunity to reinfection. We study the network SIRI (Susceptible-Infected-Recovered-Infected) model, an epidemic model for the spread of contagiou…
Susceptibility governs the dynamics of contagion. The classical SIR model is one of the simplest compartmental models of contagion spread, assuming a single shared susceptibility level. However, variation in susceptibility over a population can fundamentally affect the dynamics of contagion and thus the ultimate outcome of a pandemic. We develop mathematical machinery which explicitly considers susceptibility variation, illuminates how the susceptibility distribution is sculpted by contagion, and thence how such variation affects the SIR differential questions that govern contagion. Our method…
