Complex Contagion Research Articles

Social ageing and higher-order interactions: social selectiveness can enhance older individuals' capacity to transmit knowledge.

In long-lived organisms, experience can accumulate with age, such that older individuals may act as repositories of ecological and social knowledge. Such knowledge is often beneficial and can spread via social transmission, leading to the expectation that ageing individuals will remain socially well-integrated. However, social ageing involves multiple processes that modulate the relationship between age and social connectivity in complex ways. We developed a generative model to explore how social ageing may drive changes in social network position and shape older individuals' capacity to transmit knowledge to others. We further employ novel hypernetwork analyses that capture higher-order interactions (i.e. involving ≥ 3 participants) to reveal potential relationships between age and sociality that conventional dyadic networks may overlook. We find that older individuals in our simulations effectively facilitate transmission across a range of scenarios, especially when transmission resembles a complex contagion or when social selectivity (i.e. prioritization of key relationships) rapidly emerges with age. These patterns result from the formation of tight-knit sets of older associates that co-occur in multiple groups, thereby reinforcing one another's capacity to transmit knowledge. Our findings suggest key avenues for future empirical work and illustrate the use of hypernetworks in advancing the study of social behaviour.This article is part of the discussion meeting issue 'Understanding age and society using natural populations'.

Overdose as a complex contagion: modelling the community spread of overdose events following law enforcement efforts to disrupt the drug market

BackgroundThe opioid overdose mortality crisis in the USA is an ongoing public health epidemic. Ongoing law enforcement strategies to disrupt local unregulated drug markets can have an iatrogenic effect of...

Reconstructing networks from simple and complex contagions

Reconstructing networks from simple and complex contagions

Embeddedness, Social Contagion, and Vote Choice in the 2022 U.S. Senate Elections

The growing availability of data from social media sites has allowed for in-depth studies on online political behavior. In particular, estimating whether belief in far-right conspiracy theories leads to better or worse electoral outcomes for the Republican parties has produced conflicting results. Borrowing from the literature on complex contagion, we turn to data extracted from Twitter to study the correlation between the network of contacts of Republican users and electoral outcomes in the November 2022 U.S. Senate elections. We find that the clustering coefficient of Republican supporters is significantly and positively associated with higher levels of support for GOP candidates in these races. However, the impact of embeddedness in social networks varies depending on whether candidates in these races were explicitly endorsed by former President Donald Trump.

Unveiling the reproduction number scaling in characterizing social contagion coverage

The spreading of diseases depends critically on the reproduction number, which gives the expected number of new cases produced by infectious individuals during their lifetime. Here we reveal a widespread power-law scaling relationship between the variance and the mean of the reproduction number across simple and complex contagion mechanisms on various network structures. This scaling relation is verified on an empirical scientific collaboration network and analytically studied using generating functions. Specifically, we explore the impact of the scaling law of the reproduction number on the expected size of cascades of contagions. We find that the mean cascade size can be inferred from the mean reproduction number, albeit with limitations in capturing spreading variations. Nonetheless, insights derived from the tail of the distribution of the reproduction number contribute to explaining cascade size variation and allow the distinction between simple and complex contagion mechanisms. Our study sheds light on the intricate dynamics of spreading processes and cascade sizes in social networks, offering valuable insights for managing contagion outbreaks and optimizing responses to emerging threats.

Infection patterns in simple and complex contagion processes on networks.

Contagion processes, representing the spread of infectious diseases, information, or social behaviors, are often schematized as taking place on networks, which encode for instance the interactions between individuals. The impact of the network structure on spreading process has been widely investigated, but not the reverse question: do different processes unfolding on a given network lead to different infection patterns? How do the infection patterns depend on a model's parameters or on the nature of the contagion processes? Here we address this issue by investigating the infection patterns for a variety of models. In simple contagion processes, where contagion events involve one connection at a time, we find that the infection patterns are extremely robust across models and parameters. In complex contagion models instead, in which multiple interactions are needed for a contagion event, non-trivial dependencies on models parameters emerge, as the infection pattern depends on the interplay between pairwise and group contagions. In models involving threshold mechanisms moreover, slight parameter changes can significantly impact the spreading paths. Our results show that it is possible to study crucial features of a spread from schematized models, and inform us on the variations between spreading patterns in processes of different nature.

Patterns of stability in complex contagions

Contagions refer to the spread or transmission of diseases, behaviors, beliefs, or emotions. While some contagions easily propagate throughout entire populations, others seem to be more constrained and propagate only within specific parts of the population. This arises not just because of different transmission rates but because of qualitative differences in the mechanisms with which contagions propagate throughout a network. Diseases typically propagate through single connections, while behaviors and beliefs often necessitate multiple connections for further propagation, termed complex contagions. In this paper, we propose a graph reduction method to reduce a network to include only connections immediately relevant to the propagation of a complex contagion. Through repeated application, we obtain structures that remain stable under the reduction, allowing us to define and measure for any given network, (i) strongly contagious components, (ii) weakly contagious components, and (iii) bridge components. Information about the size and location of these components can be used as a meaningful basis to assess and prevent the potential spread of harmful contagions as well as incentivize the spread of beneficial contagions.

COMPLEX CONTAGION IN SOCIAL SYSTEMS WITH DISTRUST

Social systems are characterized by the presence of group interactions and by the existence of both trust and distrust relations. Although there is a wide literature on signed social networks, where positive signs associated to the links indicate trust, friendship, agreement, while negative signs represent distrust, antagonism, and disagreement, very little is known about the effect that signed interactions can have on the spreading of social behaviors when, not only pairwise, but also higher-order interactions are taken into account. In this paper, we introduce a model of complex contagion on signed simplicial complexes, and we investigate the role played by trust and distrust on the dynamics of a social contagion process, where exposure to multiple sources is needed for the contagion to occur. The presence of higher-order signed structures in our model naturally induces new infection and recovery mechanisms, thus increasing the richness of the contagion dynamics. Through numerical simulations and analytical results in the mean-field approximation, we show how distrust determines the way the system moves from a state where no individuals adopt the social behavior, to a state where a finite fraction of the population actively spreads it. Interestingly, we observe that the fraction of spreading individuals displays a non-monotonic dependence with respect to the average number of connections between individuals. We then investigate how social balance affects social contagion, finding that balanced triads have an ambivalent impact on the spreading process, either promoting or impeding contagion based on the relative abundance of fully trusted relations. Our results shed light on the nontrivial effect of trust on the spreading of social behaviors in systems with group interactions, paving the way to further investigations of spreading phenomena in structured populations.

Emergence of simple and complex contagion dynamics from weighted belief networks.

Social contagion is a ubiquitous and fundamental process that drives individual and social changes. Although social contagion arises as a result of cognitive processes and biases, the integration of cognitive mechanisms with the theory of social contagion remains an open challenge. In particular, studies on social phenomena usually assume contagion dynamics to be either simple or complex, rather than allowing it to emerge from cognitive mechanisms, despite empirical evidence indicating that a social system can exhibit a spectrum of contagion dynamics-from simple to complex-simultaneously. Here, we propose a model of interacting beliefs, from which both simple and complex contagion dynamics can organically arise. Our model also elucidates how a fundamental mechanism of complex contagion-resistance-can come about from cognitive mechanisms.

Stochastic modeling of cascade dynamics: A unified approach for simple and complex contagions across homogeneous and heterogeneous threshold distributions on networks.

The COVID-19 pandemic has underscored the importance of understanding, forecasting, and avoiding infectious processes, as well as the necessity for understanding the diffusion and acceptance of preventative measures. Simple contagions, like virus transmission, can spread with a single encounter, while complex contagions, such as preventive social measures (e.g., wearing masks, social distancing), may require multiple interactions to propagate. This disparity in transmission mechanisms results in differing contagion rates and contagion patterns between viruses and preventive measures. Furthermore, the dynamics of complex contagions are significantly less understood than those of simple contagions. Stochastic models, integrating inherent variability and randomness, offer a way to elucidate complex contagion dynamics. This paper introduces a stochastic model for both simple and complex contagions and assesses its efficacy against ensemble simulations for homogeneous and heterogeneous threshold configurations. The model provides a unified framework for analyzing both types of contagions, demonstrating promising outcomes across various threshold setups on Erds-Rényi graphs.

Contagion, fast and low: Modeling social influence in socio-ecological systems

The concept of contagion defines how attitudes, emotions, or behaviors spread within a specific group. Traditional models of social contagion account for network characteristics that define the spread of simple or complex ideas based on the degree of exposure of susceptible agents to their affected “contact neighborhood”. However, these models understate two principal characteristics of real-world dynamics: (i) the competition among ideas of varying degrees of complexity (as observed in voting models) and (ii) the feedback-driven evolution of contagion complexity. Certain network features (e.g., network size, topology, neighborhood size) might favor the diffusion of competing simple or complex ideas, depending on their distinct characteristics. Furthermore, the dominant behavior disseminated may alter the agent’s operational environment, thereby modifying the cost of influencing additional agents. For instance, in co-evolutionary games such as the tragedy of the commons, encouraging agents to collaborate in the context of abundant and untapped resources requires a costly and complex contagion; conversely, in situations of resource depletion, prompting agents to reduce excessive exploitation is less costly—in line with the pathway of simple contagion. In this report, we develop an agent-based model that incorporates all of these aspects.

Triadic Approximation Reveals the Role of Interaction Overlap on the Spread of Complex Contagions on Higher-Order Networks.

Contagion processes relying on the exposure to multiple sources are prevalent in social systems, and are effectively represented by hypergraphs. In this Letter, we derive a mean-field model that goes beyond node- and pair-based approximations. We reveal how the stability of the contagion-free state is decided by either two- or three-body interactions, and how this is strictly related to the degree of overlap between these interactions. Our findings demonstrate the dual effect of increased overlap: it lowers the invasion threshold, yet produces smaller outbreaks. Corroborated by numerical simulations, our results emphasize the significance of the chosen representation in describing a higher-order process.

Effectiveness of contact tracing on networks with cliques.

Contact tracing, the practice of isolating individuals who have been in contact with infected individuals, is an effective and practical way of containing disease spread. Here we show that this strategy is particularly effective in the presence of social groups: Once the disease enters a group, contact tracing not only cuts direct infection paths but can also pre-emptively quarantine group members such that it will cut indirect spreading routes. We show these results by using a deliberately stylized model that allows us to isolate the effect of contact tracing within the clique structure of the network where the contagion is spreading. This will enable us to derive mean-field approximations and epidemic thresholds to demonstrate the efficiency of contact tracing in social networks with small groups. This analysis shows that contact tracing in networks with groups is more efficient the larger the groups are. We show how these results can be understood by approximating the combination of disease spreading and contact tracing with a complex contagion process where every failed infection attempt will lead to a lower infection probability in the following attempts. Our results illustrate how contact tracing in real-world settings can be more efficient than predicted by models that treat the system as fully mixed or the network structure as locally treelike.

Hub‐and‐spoke social networks among Indonesian cocoa farmers homogenise farming practices

Abstract Smallholder farms support the livelihoods of 2.5 billion people and their decisions on how to manage their land has profound consequences for the environment and the food security of billions of people. However, farmers' values, norms and resulting management practices are usually not formed in isolation. Triangulating multiple analytical, modelling and simulation methods, we investigated if and how social influence exerted through peer‐to‐peer information exchange affect soil nutrition management among 2734 Indonesian smallholder cocoa farmers across 30 different villages. The results show that the relational structures of these village‐based social networks strongly relate to farmers' use of fertiliser. In villages with highly centralised networks (i.e. hub‐and‐spoke networks where one or very few farmers holds disproportionately central position in the village network), a large majority of farmers report the same fertiliser use, and that practice is typically to avoid using fertilisers. By contrast, in less centralised networks, fertiliser use varies widely. The observed community‐level distributions of fertiliser use can be most closely reproduced through simulations by complex contagion mechanisms in which social influence is only exerted by opinion leaders that are much more socially connected than others. However, even such leaders' abilities to influence others to change fertiliser use may be limited in practice. The combination of our quantitative and qualitative findings provides significant policy implications for development programs targeting smallholder farming communities. An important practical lesson is that common interventions which primarily engage socially central farmers may not be effective in stimulating desired transitions in social‐ecological systems. Read the free Plain Language Summary for this article on the Journal blog.

Effects of experts on the coupling dynamics of complex contagion of awareness and epidemic spreading

Effects of experts on the coupling dynamics of complex contagion of awareness and epidemic spreading

Ordering dynamics and aging in the symmetrical threshold model

The so-called Granovetter–Watts model was introduced to capture a situation in which the adoption of new ideas or technologies requires a certain redundancy in the social environment of each agent to take effect. This model has become a paradigm for complex contagion. Here we investigate a symmetric version of the model: agents may be in two states that can spread equally through the system via complex contagion. We find three possible phases: a mixed one (dynamically active disordered state), an ordered one, and a heterogeneous frozen phase. These phases exist for several configurations of the contact network. Then, we consider the effect of introducing aging as a non-Markovian mechanism in the model, where agents become increasingly resistant to change their state the longer they remain in it. We show that when aging is present, the mixed phase is replaced, for sparse networks, by a new phase with different dynamical properties. This new phase is characterized by an initial disordering stage followed by a slow ordering process toward a fully ordered absorbing state. In the ordered phase, aging modifies the dynamical properties. For random contact networks, we develop a theoretical description based on an approximate master equation that describes with good accuracy the results of numerical simulations for the model with and without aging.

On the role of diffusion dynamics on community-aware centrality measures.

Theoretical and empirical studies on diffusion models have revealed their versatile applicability across different fields, spanning from sociology and finance to biology and ecology. The presence of a community structure within real-world networks has a substantial impact on how diffusion processes unfold. Key nodes located both within and between these communities play a crucial role in initiating diffusion, and community-aware centrality measures effectively identify these nodes. While numerous diffusion models have been proposed in literature, very few studies investigate the relationship between the diffusive ability of key nodes selected by community-aware centrality measures, the distinct dynamical conditions of various models, and the diverse network topologies. By conducting a comparative evaluation across four diffusion models, utilizing both synthetic and real-world networks, along with employing two different community detection techniques, our study aims to gain deeper insights into the effectiveness and applicability of the community-aware centrality measures. Results suggest that the diffusive power of the selected nodes is affected by three main factors: the strength of the network's community structure, the internal dynamics of each diffusion model, and the budget availability. Specifically, within the category of simple contagion models, such as SI, SIR, and IC, we observe similar diffusion patterns when the network's community structure strength and budget remain constant. In contrast, the LT model, which falls under the category of complex contagion dynamics, exhibits divergent behavior under the same conditions.

Nonlinear bias toward complex contagion in uncertain transmission settings.

Current epidemics in the biological and social domains are challenging the standard assumptions of mathematical contagion models. Chief among them are the complex patterns of transmission caused by heterogeneous group sizes and infection risk varying by orders of magnitude in different settings, like indoor versus outdoor gatherings in the COVID-19 pandemic or different moderation practices in social media communities. However, quantifying these heterogeneous levels of risk is difficult, and most models typically ignore them. Here, we include these features in an epidemic model on weighted hypergraphs to capture group-specific transmission rates. We study analytically the consequences of ignoring the heterogeneous transmissibility and find an induced superlinear infection rate during the emergence of a new outbreak, even though the underlying mechanism is a simple, linear contagion. The dynamics produced at the individual and group levels are therefore more similar to complex, nonlinear contagions, thus blurring the line between simple and complex contagions in realistic settings. We support this claim by introducing a Bayesian inference framework to quantify the nonlinearity of contagion processes. We show that simple contagions on real weighted hypergraphs are systematically biased toward the superlinear regime if the heterogeneity of the weights is ignored, greatly increasing the risk of erroneous classification as complex contagions. Our results provide an important cautionary tale for the challenging task of inferring transmission mechanisms from incidence data. Yet, it also paves the way for effective models that capture complex features of epidemics through nonlinear infection rates.

A generating-function approach to modelling complex contagion on clustered networks with multi-type branching processes

Abstract Understanding cascading processes on complex network topologies is paramount for modelling how diseases, information, fake news and other media spread. In this article, we extend the multi-type branching process method developed in Keating et al., (2022), which relies on networks having homogenous node properties, to a more general class of clustered networks. Using a model of socially inspired complex contagion we obtain results, not just for the average behaviour of the cascades but for full distributions of the cascade properties. We introduce a new method for the inversion of probability generating functions to recover their underlying probability distributions; this derivation naturally extends to higher dimensions. This inversion technique is used along with the multi-type branching process to obtain univariate and bivariate distributions of cascade properties. Finally, using clique-cover methods, we apply the methodology to synthetic and real-world networks and compare the theoretical distribution of cascade sizes with the results of extensive numerical simulations.

Financial fire sales as continuous-state complex contagion

Financial fire sales as continuous-state complex contagion