arXiv subjects

Guillaume St-Onge

Publications and source records attributed to Guillaume St-Onge.

At least 19 recordsLinked to original sources

arXiv2026

The impact of behavioral homophily and conformity on epidemic spreading in networks with large groups

Understanding how social behavior influences epidemic dynamics has become a central focus in mathematical epidemiology. In particular, \textit{behavioral homophily} (the tendency of individuals to associate with similar others) and \textit{conformity} (the adjustment of individual behavior to group norms) are key mechanisms in shaping transmission patterns. In this work, we investigate the combined impact of these behavioral processes on the susceptible-infected-susceptible (SIS) dynamics on networks with large, densely connected groups, modeled as cliques. Each individual has an intrinsic behavioral preference, but their expressed behavior within a group is modulated by its composition, reflecting conformity dynamics. Using the approximate master equations (AME) framework, we characterize the interplay between behavioral heterogeneity, group structure, and epidemic localization. Our results reveal that behavioral homophily amplifies the effects of conformity in large groups, enabling minority behaviors to persist as well as substantially shifting epidemic thresholds and spreading regimes.

physics.soc-ph↗

arXiv2026

Simpson's paradox explains the ubiquity of nonlinear, threshold, and complex contagions

Complex contagions describe systems where the probability or rate of contagious transmission is a nonlinear function of the exposure to contagious agents. These models were first studied theoretically but have since been used to capture effects such as nonconformism, social reinforcement or peer pressure in empirical data. However, recent studies have shown that local correlations (e.g., group structure or temporal burstiness) and heterogeneity (e.g., diversity of parameters or covariates) can give the illusion of nonlinear effects even when the dynamics is actually linear. We briefly review these studies to inform a new model and explanation for these effective models of complex contagions. We find global threshold dynamics and superlinear complex contagions even in populations where agents are distributed across social groups described solely by linear or even sublinear contagions. This effect can be understood as a manifestation of Simpson's paradox. Incidence data from heterogeneous groups can look superlinear once averaged over all groups, since the sampling of groups represented at high incidence is biased towards those with stronger local transmission. We then define what we call a Simpson's contagion: a contagion process that looks superlinear when observed over an entire population, but is mechanistically linear or even sublinear in all of its subgroups. By exploring these Simpson's contagions over mathematical case studies, our work contributes to the growing body of literature on the ubiquity of threshold and complex contagions as effective models, and our results stress the pitfall of model selection that ignores correlations and heterogeneity in populations.

physics.soc-ph↗

arXiv2026

Group dynamics shape contagion onsets and multistable active phases under collective reinforcement

Group-based reinforcement can induce discontinuous transitions from inactive to active phases in higher-order contagion models. However, these results are typically obtained on static interaction structures or within mean-field approximations that neglect temporal changes in group composition. Here, we show that group dynamics is not a secondary effect but a central aspect that determines the macroscopic transition class of higher-order contagion processes. We develop an analytically tractable approximate master equation model that effectively interpolates between quenched and mean-field limits through a group composition turnover rate. Our results reveal the rich impact of time-varying structures: it can induce discontinuous phase transition, broaden the bistable region, and at the same time promote or suppress contagion near criticality. Moreover, when real-world turnover rates and group-size heterogeneity are taken into account, the system exhibits a qualitatively richer phase diagram with four distinct dynamical phases, combining continuous or discontinuous transitions with localized or delocalized activity. In localized regimes, we uncover multistable active phases with multiple coexisting active states, which are observed in neither the annealed nor the quenched limits, and extend classical absorbing-active bistability. Finally, we demonstrate that the emergence of discontinuous transitions in real-world systems requires stronger nonlinear reinforcement than previously thought, indicating that simulations in static structures can yield qualitatively misleading predictions.

physics.soc-ph↗

arXiv2025

One pathogen does not an epidemic make: A review of interacting contagions, diseases, beliefs, and stories

From pathogens and computer viruses to genes and memes, contagion models have found widespread utility across the natural and social sciences. Despite their success and breadth of adoption, the approach and structure of these models remain surprisingly siloed by field. Given the siloed nature of their development and widespread use, one persistent assumption is that a given contagion can be studied in isolation, independently from what else might be spreading in the population. In reality, countless contagions of biological and social nature interact within hosts (interacting with existing beliefs, or the immune system) and across hosts (interacting in the environment, or affecting transmission mechanisms). Additionally, from a modeling perspective, we know that relaxing these assumptions has profound effects on the physics and translational implications of the models. Here, we review mechanisms for interactions in social and biological contagions, as well as the models and frameworks developed to include these interactions in the study of the contagions. We highlight existing problems related to the inference of interactions and to the scalability of mathematical models and identify promising avenues of future inquiries. In doing so, we highlight the need for interdisciplinary efforts under a unified science of contagions and for removing a common dichotomy between social and biological contagions.

physics.soc-ph↗

arXiv2025

Characteristic scales and adaptation in higher-order contagions

People organize in groups and contagions spread across them. A simple stochastic process, yet complex to model due to dynamical correlations within and between groups. Moreover, groups can evolve if agents join or leave in response to contagions. To address the lack of analytical models that account for dynamical correlations and adaptation in groups, we introduce the method of generalized approximate master equations. We first analyze how nonlinear contagions differ when driven by group-level or individual-level dynamics. We then study the characteristic levels of group activity that best describe the stochastic process and that optimize agents' ability to adapt to it. Naturally lending itself to study adaptive hypergraphs, our method reveals how group structure unlocks new dynamical regimes and enables distinct suitable adaptation strategies. Our approach offers a highly accurate model of binary-state dynamics on hypergraphs, advances our understanding of contagion processes, and opens the study of adaptive group-structured systems.

physics.soc-ph↗

arXiv2023

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 novel 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.

physics.soc-ph↗

arXiv2023

Adaptive hypergraphs and the characteristic scale of higher-order contagions using generalized approximate master equations

People organize in groups and contagions spread across them. A simple process, but complex to model due to dynamical correlations within groups and between groups. Groups can also change as agents join and leave them to avoid infection. To study the characteristic levels of group activity required to best model dynamics and for agents to adapt, we develop master equations for adaptive hypergraphs, finding bistability and regimes of detrimental, beneficial, and optimal rewiring, at odds with adaptation on networks. Our study paves the way for higher-order adaptation and self-organized hypergraphs.

physics.soc-ph↗

arXiv2022

Hierarchical team structure and multidimensional localization (or siloing) on networks

Knowledge silos emerge when structural properties of organizational interaction networks limit the diffusion of information. These structural barriers are known to take many forms at different scales - hubs in otherwise sparse organisations, large dense teams, or global core-periphery structure - but we lack an understanding of how these different structures interact. Here we bridge the gap between the mathematical literature on localization of spreading dynamics and the more applied literature on knowledge silos in organizational interaction networks. To do so, we introduce a new model that considers a layered structure of teams to unveil a new form of hierarchical localization (i.e., the localization of information at the top or center of an organization) and study its interplay with known phenomena of mesoscopic localization (i.e., the localization of information in large groups), $k$-core localization (i.e., around denser $k$-cores) and hub localization (i.e., around high degree stars). We also include a complex contagion mechanism by considering a general infection kernel which can depend on hierarchical level (influence), degree (popularity), infectious neighbors (social reinforcement) or team size (importance). This general model allows us to study the multifaceted phenomenon of information siloing in complex organizational interaction networks and opens the door to new optimization problems to promote or hinder the emergence of different localization regimes.

physics.soc-ph↗

arXiv2021

Influential groups for seeding and sustaining nonlinear contagion in heterogeneous hypergraphs

Several biological and social contagion phenomena, such as superspreading events or social reinforcement, are the results of multi-body interactions, for which hypergraphs offer a natural mathematical description. In this paper, we develop a novel mathematical framework based on approximate master equations to study contagions on random hypergraphs with a heterogeneous structure, both in terms of group size (hyperedge cardinality) and of membership of nodes to groups (hyperdegree). The characterization of the inner dynamics of groups provides an accurate description of the contagion process, without losing the analytical tractability. Using a contagion model where multi-body interactions are mapped onto a nonlinear infection rate, our two main results show how large groups are influential, in the sense that they drive both the early spread of a contagion and its endemic state (i.e., its stationary state). First, we provide a detailed characterization of the phase transition, which can be continuous or discontinuous with a bistable regime, and derive analytical expressions for the critical and tricritical points. We find that large values of the third moment of the membership distribution suppress the emergence of a discontinuous phase transition. Furthermore, the combination of heterogeneous group sizes and nonlinear contagion facilitates the onset of a mesoscopic localization phase, where contagion is sustained only by the largest groups, thereby inhibiting bistability as well. Second, we formulate the problem of optimal seeding for hypergraph contagion, and we compare two strategies: tuning the allocation of seeds according to either individual node or group properties. We find that, when the contagion is sufficiently nonlinear, groups are more effective seeds of contagion than individual nodes.

physics.soc-ph↗

arXiv2021

Source-sink cooperation dynamics constrain institutional evolution in a group-structured society

Societies change through time, entailing changes in behaviors and institutions. We ask how social change occurs when behaviors and institutions are interdependent. We model a group-structured society in which the transmission of individual behavior occurs in parallel with the selection of group-level institutions. We consider a cooperative behavior that generates collective benefits for groups but does not spread between individuals on its own. Groups exhibit institutions that increase the diffusion of the behavior within the group, but also incur a group cost. Groups adopt institutions in proportion to their fitness. Finally, cooperative behavior may also spread globally. As expected, we find that cooperation and institutions are mutually reinforcing. But the model also generates behavioral source-sink dynamics when cooperation generated in institutional groups spreads to non-institutional groups, boosting their fitness. Consequently, the global diffusion of cooperation creates a pattern of institutional free-riding that limits the evolution of group-beneficial institutions. Our model suggests that, in a group-structured society, large-scale change in behavior and institutions (i.e. social change) can be best achieved when the two remain correlated, such as through the spread successful pilot programs.

physics.soc-ph↗

arXiv2021

Universal nonlinear infection kernel from heterogeneous exposure on higher-order networks

The colocation of individuals in different environments is an important prerequisite for exposure to infectious diseases on a social network. Standard epidemic models fail to capture the potential complexity of this scenario by (1) neglecting the higher-order structure of contacts which typically occur through environments like workplaces, restaurants, and households; and by (2) assuming a linear relationship between the exposure to infected contacts and the risk of infection. Here, we leverage a hypergraph model to embrace the heterogeneity of environments and the heterogeneity of individual participation in these environments. We find that combining heterogeneous exposure with the concept of minimal infective dose induces a universal nonlinear relationship between infected contacts and infection risk. Under nonlinear infection kernels, conventional epidemic wisdom breaks down with the emergence of discontinuous transitions, super-exponential spread, and hysteresis.

physics.soc-ph↗

arXiv2021

Localization, epidemic transitions, and unpredictability of multistrain epidemics with an underlying genotype network

Mathematical disease modelling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen spreading among a population. This paradigm has been useful in simplifying the biological reality of epidemics and has allowed the modelling community to focus on the complexity of other factors such as population structure and interventions. However, there is an increasing amount of evidence that the strain diversity of pathogens, and their interplay with the host immune system, can play a large role in shaping the dynamics of epidemics. Here, we introduce a disease model with an underlying genotype network to account for two important mechanisms. One, the disease can mutate along network pathways as it spreads in a host population. Two, the genotype network allows us to define a genetic distance across strains and therefore to model the transcendence of immunity often observed in real world pathogens. We study the emergence of epidemics in this model, through its epidemic phase transitions, and highlight the role of the genotype network in driving cyclicity of diseases, large scale fluctuations, sequential epidemic transitions, as well as localization around specific strains of the associated pathogen. More generally, our model illustrates the richness of behaviours that are possible even in well-mixed host populations once we consider strain diversity and go beyond the "one disease equals one pathogen" paradigm.

q-bio.PE↗

arXiv2021

Social confinement and mesoscopic localization of epidemics on networks

Recommendations around epidemics tend to focus on individual behaviors, with much less efforts attempting to guide event cancellations and other collective behaviors since most models lack the higher-order structure necessary to describe large gatherings. Through a higher-order description of contagions on networks, we model the impact of a blanket cancellation of events larger than a critical size and find that epidemics can suddenly collapse when interventions operate over groups of individuals rather than at the level of individuals. We relate this phenomenon to the onset of mesoscopic localization, where contagions concentrate around dominant groups.

physics.soc-ph↗

arXiv2020

Inference for growing trees

One can often make inferences about a growing network from its current state alone. For example, it is generally possible to determine how a network changed over time or pick among plausible mechanisms explaining its growth. In practice, however, the extent to which such problems can be solved is limited by existing techniques, which are often inexact, inefficient, or both. In this article we derive exact and efficient inference methods for growing trees and demonstrate them in a series of applications: network interpolation, history reconstruction, model fitting, and model selection.

cs.SI↗

arXiv2020

Master equation analysis of mesoscopic localization in contagion dynamics on higher-order networks

Simple models of infectious diseases tend to assume random mixing of individuals, but real interactions are not random pairwise encounters: they occur within various types of gatherings such as workplaces, households, schools, and concerts, best described by a higher-order network structure. We model contagions on higher-order networks using group-based approximate master equations, in which we track all states and interactions within a group of nodes and assume a mean-field coupling between them. Using the Susceptible-Infected-Susceptible dynamics, our approach reveals the existence of a mesoscopic localization regime, where a disease can concentrate and self-sustain only around large groups in the network overall organization. In this regime, the phase transition is smeared, characterized by an inhomogeneous activation of the groups. At the mesoscopic level, we observe that the distribution of infected nodes within groups of a same size can be very dispersed, even bimodal. When considering heterogeneous networks, both at the level of nodes and groups, we characterize analytically the region associated with mesoscopic localization in the structural parameter space. We put in perspective this phenomenon with eigenvector localization and discuss how a focus on higher-order structures is needed to discern the more subtle localization at the mesoscopic level. Finally, we discuss how mesoscopic localization affects the response to structural interventions and how this framework could provide important insights for a broad range of dynamics.

physics.soc-ph↗

arXiv2020

Threefold way to the dimension reduction of dynamics on networks: an application to synchronization

Several complex systems can be modeled as large networks in which the state of the nodes continuously evolves through interactions among neighboring nodes, forming a high-dimensional nonlinear dynamical system. One of the main challenges of Network Science consists in predicting the impact of network topology and dynamics on the evolution of the states and, especially, on the emergence of collective phenomena, such as synchronization. We address this problem by proposing a Dynamics Approximate Reduction Technique (DART) that maps high-dimensional (complete) dynamics unto low-dimensional (reduced) dynamics while preserving the most salient features, both topological and dynamical, of the original system. DART generalizes recent approaches for dimension reduction by allowing the treatment of complex-valued dynamical variables, heterogeneities in the intrinsic properties of the nodes as well as modular networks with strongly interacting communities. Most importantly, we identify three major reduction procedures whose relative accuracy depends on whether the evolution of the states is mainly determined by the intrinsic dynamics, the degree sequence, or the adjacency matrix. We use phase synchronization of oscillator networks as a benchmark for our threefold method. We successfully predict the synchronization curves for three phase dynamics (Winfree, Kuramoto, theta) on the stochastic block model. Moreover, we obtain the bifurcations of the Kuramoto-Sakaguchi model on the mean stochastic block model with asymmetric blocks and we show numerically the existence of periphery chimera state on the two-star graph. This allows us to highlight the critical role played by the asymmetry of community sizes on the existence of chimera states. Finally, we systematically recover well-known analytical results on explosive synchronization by using DART for the Kuramoto-Sakaguchi model on the star graph.

nlin.AO↗

arXiv2020

Network comparison and the within-ensemble graph distance

Quantifying the differences between networks is a challenging and ever-present problem in network science. In recent years a multitude of diverse, ad hoc solutions to this problem have been introduced. Here we propose that simple and well-understood ensembles of random networks (such as Erdős-Rényi graphs, random geometric graphs, Watts-Strogatz graphs, the configuration model, and preferential attachment networks) are natural benchmarks for network comparison methods. Moreover, we show that the expected distance between two networks independently sampled from a generative model is a useful property that encapsulates many key features of that model. To illustrate our results, we calculate this within-ensemble graph distance and related quantities for classic network models (and several parameterizations thereof) using 20 distance measures commonly used to compare graphs. The within-ensemble graph distance provides a new framework for developers of graph distances to better understand their creations and for practitioners to better choose an appropriate tool for their particular task.

physics.soc-ph↗

arXiv2020

Detecting structural perturbations from time series with deep learning

Small disturbances can trigger functional breakdowns in complex systems. A challenging task is to infer the structural cause of a disturbance in a networked system, soon enough to prevent a catastrophe. We present a graph neural network approach, borrowed from the deep learning paradigm, to infer structural perturbations from functional time series. We show our data-driven approach outperforms typical reconstruction methods while meeting the accuracy of Bayesian inference. We validate the versatility and performance of our approach with epidemic spreading, population dynamics, and neural dynamics, on various network structures: random networks, scale-free networks, 25 real food-web systems, and the C. Elegans connectome. Moreover, we report that our approach is robust to data corruption. This work uncovers a practical avenue to study the resilience of real-world complex systems.

physics.soc-ph↗