arXiv subjects

Alex Arenas

Publications and source records attributed to Alex Arenas.

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

Emergent Self-Attention from Astrocyte-Gated Associative Memory Dynamics

We introduce a Hopfield-type associative memory in which effective connectivity is multiplicatively modulated by astrocytic gains evolving under an entropy-regularized replicator equation. The coupled neuron-astrocyte dynamics admit a Lyapunov function, ensuring global convergence. At fixed points, astrocytic gains implement a softmax-normalized allocation over pattern similarity scores, yielding a mechanistic realization of self-attention as emergent routing on the gain simplex. In regimes of high memory load and interference, the model significantly improves retrieval accuracy relative to classical Hopfield dynamics and recent neuron-astrocyte baselines. These results establish a dynamical systems framework linking glial modulation, competitive resource allocation, and attention-like computation.

physics.data-an↗

arXiv2026

Cycle holonomy captures higher-order compatibility constraints in remote synchronization

Higher-order interactions have typically been modeled using hypergraphs or simplicial complexes, where interactions explicitly involve more than two nodes. Here we demonstrate that effective higher-order dynamical constraints emerge naturally on ordinary graphs, provided the interaction carries nontrivial topological structure. We study a gauge-coupled phase model with edge phase lags whose accumulation around closed loops produces gauge-invariant mismatches. We show that the associated twisted Laplacian admits a zero mode if and only if all cycle holonomies vanish. Consequently, global compatibility is obstructed not by local pairwise mismatches, but by intrinsic topological frustration on cycles. We then connect this framework to the symmetric Sakaguchi--Kuramoto model, whose local coupling law differs from the gauge-coupled model but whose node phases impose cycle closure on physical phase differences. For cactus graphs, path mismatches induced by the symmetric lag can be represented through associated cycle holonomies, providing a static spectral encoding of their global residual incompatibility. Our results establish a spectral framework linking frustration to cycle-level constraints and identify cycle holonomy as a local-to-global diagnostic of path incompatibility in synchronization dynamics.

physics.soc-ph↗

arXiv2026

A convex-geometric framework for fully phase-locked states in the finite Kuramoto model

We study the finite-size Kuramoto model of all-to-all coupled phase oscillators with heterogeneous natural frequencies and characterize the minimal coupling strength required for the existence of a fully phase-locked equilibrium (in a co-rotating frame). To remove the degeneracy due to uniform phase shifts, we move to a reduced co-rotating frame and assess stability through the Jacobian of the reduced system: a fully phase-locked state is stable when this Jacobian is negative definite. This defines a stability region in the phase space. The Kuramoto vector field maps this region to a convex set in frequency space, so a fully-locked state at coupling $K$ exists exactly when the rescaled frequency vector $\hat{\mathbf{\omega}}/K$ lies inside that convex image. The critical coupling $K_{\ell}$ is defined as the smallest coupling strength for which a fully phase-locked equilibrium exists; geometrically, it corresponds to the first intersection of the ray $t\hat{\mathbf{\omega}}$ with the boundary of this convex set. Building on this convex-geometric structure, we construct an explicit polytope from analytically computable boundary points of the stability region, providing a closed-form upper bound $K_b \ge K_{\ell}$. The bound is exact for frequencies aligned with polytope vertices and offers a fully explicit outer approximation for general frequency vectors. While not uniformly sharp in a quantitative sense, this construction exposes the underlying geometry of stable fully phase-locking solutions. These results provide a practical use the convex-geometric structure underlying stable fully-locked states in the Kuramoto model.

physics.soc-ph↗

arXiv2026

Interplay between evolutionary and epidemic time scales challenges the outcome of control policies

The SIR model is the cornerstone model for mathematical epidemiology, explaining key epidemic features such as the second-order transition between disease-free and epidemic states, the initial exponential growth of outbreaks or the short-term benefits of control measures. Nonetheless, the classical SIR model assumes that pathogen traits remain fixed, thus neglecting viral evolution. Here we propose a minimal extension of the SIR model, allowing infectiousness to evolve. We show that such evolution can cause superexponential early growth of outbreaks, create abrupt epidemic transitions, and undermine the effectiveness of control policies, as lifting interventions too early can lead to worse epidemic scenarios than no action. We derive analytical expressions for the critical mutation rate and intervention time governing this behavior, and identify a strong asymmetry between control strategies: while shortening the infectious period hinders transmission without suppressing viral evolution, lowering transmission both reduces cases and slows down viral evolution.

q-bio.PE↗

arXiv2026

Nonlinear competition avoidance favors coexistence in microbial populations

Bacteria regulate their motility through a variety of mechanisms, including quorum sensing (QS) and other density-dependent responses mediated by diffusible signals. While nonlinear density-dependent motility is well known in active-matter theory to generate nonequilibrium spatial patterns, its consequences for the coexistence of growing, interacting species remain less explored. Here we develop a minimal spatially structured model for two strongly competing species in which local demographic interactions are coupled to an escape response: each species increases its motility nonlinearly (sigmoidal) with the local abundance of its competitor. We show that this sigmoidal motility regulation promotes optimal spatial self-organization and can sustain long term coexistence via segregation, even in parameter regimes that yield competitive exclusion in well-mixed Lotka-Volterra dynamics. On two-dimensional lattices, the interplay between demographic competition and density-dependent motility generates a range of emergent patterns, including regimes in which the weaker competitor counterintuitively has higher total abundance. Overall, our results identify nonlinear, competitor-induced motility as a fundamental mechanism capable of sustaining coexistence in competing microbial populations.

q-bio.PE↗

arXiv2026

Decentralization can hinder frequency synchronization in power grids through multiple phase transitions

Decarbonization is rapidly increasing the penetration of inverter-based renewables and other low-capacity generators, intensifying concerns about frequency synchronization in increasingly decentralized power grids. A common heuristic from Kuramoto onset theory and homogeneous parameter swing-equation models is that distributing generation across many smaller units reduces the effective heterogeneity of nodal injections (natural frequencies) and lowers the coupling required for synchronization. Here, using a second-order Kuramoto model, we investigate how decentralization affects frequency synchronization when inertia and damping scale with power generation and consumption. We find that decentralization does not always lower the critical frequency synchronization threshold. Instead, increasing decentralization can induce a non-monotonic dependence of the critical coupling strength and lead to a double phase transition in frequency synchronization. These behaviors remain robust under asymmetric inertia between consumers and generators. Even when empirical power-generation and power-consumption distributions are considered, a region in which the critical threshold remains nearly constant is observed as decentralization increases. Our results demonstrate that decentralization can give rise to complex collective dynamics and caution against assuming that decentralization alone ensures improved frequency synchronization.

physics.soc-ph↗

arXiv2025

Structured Interactions Drive Abrupt Transitions in the Spatial Organization of Microbial Communities

Bacteria possess diverse mechanisms to regulate their motility in response to environmental and physiological signals, enabling them to navigate complex habitats and adapt their behavior. Among these mechanisms, interspecies recognition enables cells to modulate their movement based on the ecological identity of neighboring species. Here, we introduce a model in which we assume bacterial species recognizes each other and interact via local signals that either enhance or suppress the motility of neighboring cells. Through large-scale simulations and a coarse-grained stochastic model, we demonstrate the emergence of a sharp transition driven by nucleation processes: increasing the density of motility-suppressing interactions drives the system from a fully mixed, motile phase to a state characterized by large, stationary bacterial clusters. Remarkably, in systems with a large number of interacting species, this transition can be triggered solely by altering the structure of the motility-regulation interaction matrix while maintaining species and interaction densities constant. In particular, we find that heterogeneous and modular interactions promote the transition more readily than homogeneous random ones. These results contribute to the ongoing effort to understand microbial interactions, suggesting that structured, non-random ones may be key to reproducing commonly observed spatial patterns in microbial communities.

q-bio.PE↗

arXiv2025

Genotype networks drive oscillating endemicity and epidemic trajectories in viral evolution

Rapidly evolving viruses use antigenic drift as a key mechanism to evade host immunity and persist in real populations. While traditional models of antigenic drift and epidemic spread rely on low-dimensional antigenic spaces, genomic surveillance data reveal that viral evolution produces complex antigenic genotype networks with hierarchical modular structures. In this study, we present an eco-evolutionary framework in which viral evolution and population immunity dynamics are shaped by the structure of antigenic genotype networks. Using synthetic networks, we demonstrate that network topology alone can drive transitions between stable endemic states and recurrent seasonal epidemics. Furthermore, our results show how the integration of the genotype network of the H3N2 influenza in our model allows for estimating the emergence times of various haplotypes resulting from its evolution. Our findings underscore the critical role of the topology of genotype networks in shaping epidemic behavior and, besides, provide a robust framework for integrating real-world genomic data into predictive epidemic models.

q-bio.PE↗

arXiv2025

Network-Driven Vaccination Strategies for Preventing Rebound Dynamics in Metapopulation Epidemic Control

A critical question in epidemic control concerns the minimal requirements for a vaccination campaign to effectively halt a contagion process. However, control measures can inadvertently trigger resurgence dynamics, driven by a reservoir of susceptible individuals left unexposed in the controlled wave. This phenomenon, known as the "rebound effect", is often preceded by a temporary drop in cases, termed usually as the "honeymoon period". In this study, we examine the fundamental conditions for rebound dynamics within a metapopulation network framework. By elucidating the mechanisms underlying rebound events, we derive a rigorous mathematical criterion that identifies, based solely on the metapopulation network structure, the specific vaccination strategies likely to precipitate a rebound. Additionally, we propose an alternative vaccination protocol designed to eliminate rebound dynamics entirely. This approach is analytically validated and offers a robust pathway toward sustainable epidemic control.

physics.soc-ph↗

arXiv2024

Towards a Theory for the Formation of Chimera Patterns in Complex Networks

Chimera states, marked by the coexistence of order and disorder in systems of coupled oscillators, have captivated researchers with their existence and intricate patterns. Despite ongoing advances, a fully understanding of the genesis of chimera states remains challenging. This work formalizes a systematic method by evoking pattern formation theory to explain the emergence of chimera states in complex networks, in a similar way to how Turing patterns are produced. Employing linear stability analysis and the spectral properties of complex networks, we show that the randomness of network topology, as reflected in the localization of the graph Laplacian eigenvectors, determines the emergence of chimera patterns, underscoring the critical role of network structure. In particular, this approach explains how amplitude and phase chimeras arise separately and explores whether phase chimeras can be chaotic or not. Our findings suggest that chimeras result from the interplay between local and global dynamics at different time scales. Validated through simulations and empirical network analyses, our method enriches the understanding of coupled oscillator dynamics.

nlin.AO↗

arXiv2024

Rebound in epidemic control: How misaligned vaccination timing amplifies infection peaks

In this study, we explore the dynamic interplay between the timing of vaccination campaigns and the trajectory of disease spread in a population. Through comprehensive data analysis and modeling, we have uncovered a counter-intuitive phenomenon: initiating a vaccination process at an inopportune moment can paradoxically result in a more pronounced second peak of infections. This "rebound" phenomenon challenges the conventional understanding of vaccination impacts on epidemic dynamics. We provide a detailed examination of how improperly timed vaccination efforts can inadvertently reduce the overall immunity level in a population, considering both natural and vaccine-induced immunity. Our findings reveal that such a decrease in population-wide immunity can lead to a delayed, yet more severe, resurgence of cases. This study not only adds a critical dimension to our understanding of vaccination strategies in controlling pandemics but also underscores the necessity for strategically timed interventions to optimize public health outcomes. Furthermore, we compute which vaccination strategies are optimal for a COVID-19 tailored mathematical model, and find that there are two types of optimal strategies. The first type prioritizes vaccinating early and rapidly to reduce the number of deaths, while the second type acts later and more slowly to reduce the number of cases; both of them target primarily the elderly population. Our results hold significant implications for the formulation of vaccination policies, particularly in the context of rapidly evolving infectious diseases.

physics.soc-ph↗

arXiv2024

Human behavior-driven epidemic surveillance in urban landscapes

We introduce a surveillance strategy specifically designed for urban areas to enhance preparedness and response to disease outbreaks by leveraging the unique characteristics of human behavior within urban contexts. By integrating data on individual residences and travel patterns, we construct a Mixing matrix that facilitates the identification of critical pathways that ease pathogen transmission across urban landscapes enabling targeted testing strategies. Our approach not only enhances public health systems' ability to provide early epidemiological alerts but also underscores the variability in strategy effectiveness based on urban layout. We prove the feasibility of our mobility-informed policies by mapping essential mobility flows to major transit stations, showing that few resources focused on specific stations yields a more effective surveillance than non-targeted approaches. This study emphasizes the critical role of integrating human behavioral patterns into epidemic management strategies to improve the preparedness and resilience of major cities against future outbreaks.

physics.soc-ph↗

arXiv2024

Exploring Spatial Segregation Induced by Competition Avoidance as Driving Mechanism for Emergent Coexistence in Microbial Communities

This study investigates the role of spatial segregation, prompted by competition avoidance, as a key mechanism for emergent coexistence within microbial communities. Recognizing these communities as complex adaptive systems, we challenge the sufficiency of mean-field pairwise interaction models and consider the impact of spatial dynamics. We developed an individual-based spatial simulation depicting bacterial movement through a pattern of random walks influenced by competition avoidance, leading to the formation of spatially segregated clusters. This model was integrated with a Lotka-Volterra metapopulation framework focused on competitive interactions. Our findings reveal that spatial segregation combined with low diffusion rates and high compositional heterogeneity among patches can lead to emergent coexistence in microbial communities. This reveals a novel mechanism underpinning the formation of stable, coexisting microbe clusters, which is nonetheless incapable of promoting coexistence in the case of isolated pairs of species. This study underscores the importance of considering spatial factors in understanding the dynamics of microbial ecosystems.

physics.soc-ph↗

arXiv2023

Pattern formation and bifurcation analysis of delay induced fractional-order epidemic spreading on networks

The spontaneous emergence of ordered structures, known as Turing patterns, in complex networks is a phenomenon that holds potential applications across diverse scientific fields, including biology, chemistry, and physics. Here, we present a novel delayed fractional-order susceptible-infected-recovered-susceptible (SIRS) reaction-diffusion model functioning on a network, which is typically used to simulate disease transmission but can also model rumor propagation in social contexts. Our theoretical analysis establishes the Turing instability resulting from delay, and we support our conclusions through numerical experiments. We identify the unique impacts of delay, average network degree, and diffusion rate on pattern formation. The primary outcomes of our study are: (i) Delays cause system instability, mainly evidenced by periodic temporal fluctuations; (ii) The average network degree produces periodic oscillatory states in uneven spatial distributions; (iii) The combined influence of diffusion rate and delay results in irregular oscillations in both time and space. However, we also find that fractional-order can suppress the formation of spatiotemporal patterns. These findings are crucial for comprehending the impact of network structure on the dynamics of fractional-order systems.

physics.soc-ph↗

arXiv2023

A 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.

physics.soc-ph↗

arXiv2022

Spreading dynamics in networks under context-dependent behavior

In some systems, the behavior of the constituent units can create a `context' that modifies the direct interactions among them. This mechanism of indirect modification inspired us to develop a minimal model of context-dependent spreading. In our model, agents actively impede (favor) or not diffusion during an interaction, depending on the behavior they observe among all the peers in the group within which that interaction occurs. We divide the population into two behavioral types and provide a mean-field theory to parametrize mixing patterns of arbitrary type-assortativity within groups of any size. As an application, we examine an epidemic spreading model with context-dependent adoption of prophylactic tools such as face-masks. By analyzing the distributions of groups' size and type-composition, we uncover a rich phenomenology for the basic reproduction number and the endemic state. We analytically show how changing the group organization of contacts can either facilitate or hinder epidemic spreading, eventually moving the system from the subcritical to the supercritical phase and vice versa, depending mainly on sociological factors, such as whether the prophylactic behavior is hardly or easily induced. More generally, our work provides a theoretical foundation to model higher-order contexts and analyze their dynamical implications, envisioning a broad theory of context-dependent interactions that would allow for a new systematic investigation of a variety of complex systems.

physics.soc-ph↗

arXiv2022

Bifurcation analysis of the Microscopic Markov Chain Approach to contact-based epidemic spreading in networks

The dynamics of many epidemic compartmental models for infectious diseases that spread in a single host population present a second-order phase transition. This transition occurs as a function of the infectivity parameter, from the absence of infected individuals to an endemic state. Here, we study this transition, from the perspective of dynamical systems, for a discrete-time compartmental epidemic model known as Microscopic Markov Chain Approach, whose applicability for forecasting future scenarios of epidemic spreading has been proved very useful during the COVID-19 pandemic. We show that there is an endemic state which is stable and a global attractor and that its existence is a consequence of a transcritical bifurcation. This mathematical analysis grounds the results of the model in practical applications.

physics.soc-ph↗