Simple Contagions Research Articles

Reconstructing networks from simple and complex contagions

Reconstructing networks from simple and complex contagions

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.

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.

Simplicially driven simple contagion

Single contagion processes are known to display a continuous transition from an epidemic-free phase at low contagion rates to the epidemic state for rates above a critical threshold. This transition can become discontinuous when two simple contagion processes are coupled in a bi-directional symmetric way. However, in many cases, the coupling is not symmetric and the processes can be of a different nature. For example, risky social behaviors -- such as not wearing masks or engaging in large gatherings -- can affect the spread of a disease, and their adoption dynamics via social reinforcement mechanisms are better described by complex contagion models, rather than by the simple contagion paradigm, which is more appropriate for disease spreading phenomena. Motivated by this example, we consider a simplicial contagion (describing the adoption of a behavior) that uni-directionally drives a simple contagion (describing a disease propagation). We show that, above a critical driving strength, such driven simple contagion can exhibit both discontinuous transitions and bi-stability, which are instead absent in standard simple contagions. We provide a mean-field analytical description of the phase diagram of the system, and complement the results with Markov-chain simulations. Our results provide a novel route for a simple contagion process to display the phenomenology of a higher-order contagion, through a driving mechanism that may be hidden or unobservable in many practical instances.

Information access equality on generative models of complex networks

It is well known that networks generated by common mechanisms such as preferential attachment and homophily can disadvantage the minority group by limiting their ability to establish links with the majority group. This has the effect of limiting minority nodes’ access to information. We present the results of an empirical study on the equality of information access in network models with different growth mechanisms and spreading processes. For growth mechanisms, we focus on the majority/minority dichotomy, homophily, preferential attachment, and diversity. For spreading processes, we investigate simple versus complex contagions, different transmission rates within and between groups, and various seeding conditions. We observe two phenomena. First, information access equality is a complex interplay between network structures and the spreading processes. Second, there is a trade-off between equality and efficiency of information access under certain circumstances (e.g., when inter-group edges are low and information transmits asymmetrically). Our findings can be used to make recommendations for mechanistic design of social networks with information access equality.

Information Access Equality on Network Generative Models

It is well known that networks generated by common mechanisms such as preferential attachment and homophily can disadvantage the minority group by limiting their ability to establish links with the majority group. This has the effect of limiting minority nodes' access to information. We present the results of an empirical study on the equality of information access in network models with different growth mechanisms and spreading processes. For growth mechanisms, we focus on the majority/minority dichotomy, homophily, preferential attachment, and diversity. For spreading processes, we investigate simple vs. complex contagions, different transmission rates within and between groups, and various seeding conditions. We observe two phenomena. First, information access equality is a complex interplay between network structures and the spreading processes. Second, there is a trade-off between equality and efficiency of information access under certain circumstances (e.g., when inter-group edges are low and information transmits asymmetrically). Our findings can be used to make recommendations for mechanistic design of social networks with information access equality.

Macroscopic patterns of interacting contagions are indistinguishable from social reinforcement.

From fake news to innovative technologies, many contagions spread as complex contagions via a process of social reinforcement, where multiple exposures are distinct from prolonged exposure to a single source.1 Contrarily, biological agents such as Ebola or measles are typically thought to spread as simple contagions.2 Here, we demonstrate that these different spreading mechanisms can have indistinguishable population-level dynamics once multiple contagions interact. In the social context, our results highlight the challenge of identifying and quantifying spreading mechanisms, such as social reinforcement,3 in a world where an innumerable amount of ideas, memes and behaviors interact. In the biological context, this parallel allows the use of complex contagions to effectively quantify the non-trivial interactions of infectious diseases.

Predicting the Speed of Epidemics Spreading in Networks.

Global transport and communication networks enable information, ideas, and infectious diseases to now spread at speeds far beyond what has historically been possible. To effectively monitor, design, or intervene in such epidemic-like processes, there is a need to predict the speed of a particular contagion in a particular network, and to distinguish between nodes that are more likely to become infected sooner or later during an outbreak. Here, we study these quantities using a message-passing approach to derive simple and effective predictions that are validated against epidemic simulations on a variety of real-world networks with good agreement. In addition to individualized predictions for different nodes, we find an overall sudden transition from low density to almost full network saturation as the contagion progresses in time. Our theory is developed and explained in the setting of simple contagions on treelike networks, but we are also able to show how the method extends remarkably well to complex contagions and highly clustered networks.

EoN (Epidemics on Networks): a fast, flexible Python package for simulation, analytic approximation, and analysis of epidemics on networks

We provide a description of the Epidemics on Networks (EoN) python package designed for studying disease spread in static networks. The package consists of over $100$ methods available for users to perform stochastic simulation of a range of different processes including SIS and SIR disease, and generic simple or comlex contagions.

Concurrency and reachability in treelike temporal networks

Network properties govern the rate and extent of various spreading processes, from simple contagions to complex cascades. Recently, the analysis of spreading processes has been extended from static networks to temporal networks, where nodes and links appear and disappear. We focus on the effects of accessibility, whether there is a temporally consistent path from one node to another, and reachability, the density of the corresponding accessibility graph representation of the temporal network. The level of reachability thus inherently limits the possible extent of any spreading process on the temporal network. We study reachability in terms of the overall levels of temporal concurrency between edges and the structural cohesion of the network agglomerating over all edges. We use simulation results and develop heterogeneous mean-field model predictions for random networks to better quantify how the properties of the underlying temporal network regulate reachability.

Considering Complexity: Animal Social Networks and Behavioural Contagions

The spread of behaviours through animal social networks have often been considered as 'simple contagions'. However, research across other disciplines now provides substantial grounding for the 'complex contagion' of behaviours. The study of animal behaviour could benefit greatly from generally expanding to incorporate these new insights.

Diffusion with social reinforcement: The role of individual preferences.

The debate on diffusion in social networks has traditionally focused on the structure of the network to understand the efficiency of a network in terms of diffusion. Recently, the role of social reinforcement has been added to the debate, as it has been proposed that simple contagions diffuse better in random networks and complex contagions diffuse better in regular networks. In this paper, we show that individual preferences cannot be overlooked: complex contagions diffuse better in regular networks only if the large majority of the population is biased against adoption.

A meme propagation model to combine social affirmation with meme attractiveness and persistence

The propagation of memes on online social networks often depends on the mechanism of social affirmation. Centola termed such social-affirmation-driven diffusion as complex contagion and partly validated it through an online experiment. However, for actual online meme propagation, the mechanism of social affirmation often takes effect in combination with various other factors and mechanisms. In this paper, we examine the combinatorial effects of social affirmation and the attractiveness and persistence of the meme by proposing and analyzing a UACI model, where an agent’s activities to receive and transfer a meme is associated with the transition between its four possible states of “Uninformed”, “Attended”,“Convinced” and “Immune”. The numerical simulations illustrate nontrivial patterns of propagation. Especially, it is revealed that the effects of simple and complex contagions co-exist and equilibrate in accordance with the joint functions of meme attractiveness and social affirmation. Furthermore, the low-persistence of the meme hinders the propagation-scale more remarkably on the regular network than on the random one, indicating that the persistence may be critical for retaining complex contagion.

Virality Prediction and Community Structure in Social Networks

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 spread like complex contagions, a few viral memes spread across many communities, like diseases. We demonstrate that the future popularity of a meme can be predicted by quantifying its early spreading pattern in terms of community concentration. The more communities a meme permeates, the more viral it is. We present a practical method to translate data about community structure into predictive knowledge about what information will spread widely. This connection contributes to our understanding in computational social science, social media analytics, and marketing applications.

Failure in Complex Social Networks

A class of inhomogenously wired networks called “scale-free” networks have been shown to be more robust against failure than more homogenously connected exponential networks. The robustness of scale-free networks consists in their ability to remain connected even when failure occurs. The diffusion of information and disease across a network only requires a single contact between nodes, making network connectivity the crucial determinant of whether or not these “simple contagions” will spread. However, for “complex contagions,” such as social movements, collective behaviors, and cultural and social norms, multiple reinforcing ties are needed to support the spread of a behavior diffusion. I show that scale-free networks are much less robust than exponential networks for the spread of complex contagions, which highlights the value of more homogenously distributed social networks for the robust transmission of collective behavior.