arXiv subjects

István Z. Kiss

Publications and source records attributed to István Z. Kiss.

At least 19 recordsLinked to original sources

arXiv2026

Fast-variable reduction to complex contagion unifies epidemic models

Across biological and social complex systems, models of epidemics or contagions incorporate complexity through network correlations, adaptive behavior, higher-order interactions, or co-circulating strains. Tracking these mechanisms lead to high-dimensional mathematical systems that resist analytical treatment. We show that a broad class of models admits a systematic reduction via fast-variable elimination. The central insight is that complexity can be captured by fast variables equilibrating much faster than the epidemic, leading to ``emergent complex contagion'' where the force of infection depends on prevalence. The epidemic transition follows a universal equation and is continuous or discontinuous whether the force of infection decays or intensifies with prevalence. Our results reveal diverse epidemic models share a common skeleton such that mechanisms that share a characteristic form can be macroscopically indistinguishable.

physics.soc-ph↗

arXiv2026

Higher-order phase reduction captures delay-dependent synchronization phenomena in physical oscillator networks

Coupled oscillators with time-delayed network interactions are critical to understand synchronization phenomena in many physical systems. Phase reductions to finite-dimensional phase oscillator networks yield explicit insights into their dynamics. However, first-order phase approximations - in which the time delay acts as a phase shift - fail to capture the delay-dependence of synchronization. We develop a systematic approach to derive phase reductions for delay-coupled oscillators to higher order. Beyond first order, already a second-order phase reduction captures delay-induced synchronization as demonstrated in coupled Stuart-Landau oscillators and experiments with delay-coupled electrochemical oscillators. Our results establish a general mechanism by which time delays reshape synchronization phenomena and reveal intrinsic limitations of widely used reduced phase models, with implications for a broad range of oscillator networks.

math.DS↗

arXiv2026

Nested hyperedges promote the onset of collective transitions but suppress explosive behavior

Higher-order interactions can induce abrupt collective transitions, yet the microscopic mechanisms controlling macroscopic critical behavior remain unclear. Here we show that nested hyperedges generate a dual effect on dynamical processes: they promote the onset of collective behavior while suppressing the explosive transitions driven by higher-order feedback. To uncover the mechanism, we develop an analytically tractable theory of contagion on hypergraphs that explicitly tracks nestedness between groups of different sizes, allowing us to identify the microscopic mechanism responsible for this dual behavior. By disentangling contagion pathways, we find that nestedness redirects transmission from external links to internal, group-embedded routes -- boosting early activation but making dyadic and triadic channels increasingly redundant. This loss of structural independence quenches the nonlinear amplification required for bistability, progressively smoothing the transition as hyperedges become nested. The phenomenology holds for groups of any size, and is not specific to spreading dynamics but also emerges in higher-order Ising and Kuramoto dynamics. Overall, our results identify nestedness between group interactions as a general structural mechanism governing critical transitions in complex systems.

physics.soc-ph↗

arXiv2026

Unveiling the impact of cross-order hyperdegree correlations in contagion processes on hypergraphs

Contagion processes in social systems often involve interactions that go beyond pairwise contacts. Higher-order networks, represented as hypergraphs, have been widely used to model multi-body interactions, and their presence can drastically alter contagion dynamics compared to traditional network models. However, existing analytical approaches typically assume independence between pairwise and higher-order degrees, and thus study their roles in isolation. In this paper, we develop an effective hyperdegree model (EHDM) to describe Susceptible-Infected-Susceptible (SIS) dynamics on hypergraphs that explicitly captures correlations between the distribution of groups with different sizes. Our effective hyperdegree model shows excellent agreement with stochastic simulations across different types of higher-order networks, including those with heterogeneous degree distributions. We explore the critical role of cross-order degree correlations, specifically, whether nodes that are hubs in pairwise interactions also serve as hubs in higher-order interactions. We show that positive correlation decreases the epidemic threshold and anti-correlation temporally desynchronizes infection pathways (pairwise and group interactions). Finally, we demonstrate that, depending on the level of correlation, the optimal control strategy shifts -- from one that is purely pairwise- or higher-order-focused to one in which a mixed strategy becomes optimal.

physics.soc-ph↗

arXiv2026

Reconstructing MSM Sexual Networks to Guide PrEP Distribution Strategies for HIV Prevention

Men who have sex with men (MSM) remain disproportionately affected by HIV, yet optimizing Pre-exposure Prophylaxis (PrEP) distribution remains a public health challenge. Current guidelines and most modelling studies do not incorporate sociodemographic or network-level factors that shape transmission. While network reconstruction from egocentric data has been studied, the relative importance of demographic mixing dimensions remains uncertain. Using data from 4,667 MSM participants, we show that uncertainty in network reconstruction from egocentric survey data - specifically whether assortativity by age or race is incorporated - affects simulated HIV prevalence under the same observed PrEP uptake. We simulate HIV transmission over 50 years across this structural space and evaluate whether empirically observed uptake reaches transmission-critical network positions. Network structure strongly influences outcomes: assortative by degree networks show 17% lower equilibrium prevalence due to hub isolation within communities. Targeted PrEP strategies based on degree or k-shell centrality achieved the highest prevalence reductions, particularly in assortative by age and race networks where hubs bridge demographic groups. PrEP uptake from data is suboptimal in assortative by age and race networks, underperforming compared with network-based strategies. Results demonstrate that uncertainty in network reconstruction affects intervention design and highlight the need for robust prevention strategies under structural ambiguity.

physics.soc-ph↗

arXiv2026

To trace or not to trace: analytical insights from network-based contact-tracing models

Contact tracing is one of the most important control measures deployed during epidemics. Relying on the identification of contacts of known infected individuals, it necessitates a network perspective. Although pairwise models have been used extensively to study contact tracing, their analysis typically depends on a decoupling assumption-most commonly that contact tracing operates on a much faster timescale than disease transmission. Furthermore, contact tracing models often assume that all infected individuals become contact tracing-triggering, which is unrealistic given partial compliance to treatment. We relax both of these restrictive assumptions and provide a full analytical characterisation of the epidemic threshold in the pairwise mean-field model. Our analysis uses a fast-variables approach that captures the rapid early stabilisation of key network quantities. Inspired by mechanisms from social adoption dynamics, we introduce triplewise contact tracing in which an infected individual can be traced not only through direct contact with a single tracing-triggering neighbor (pairwise tracing), but also indirectly when connected to two tracing-triggering nodes simultaneously. For pure pairwise and pure triplewise contact tracing, we derive analytical expressions for critical contact tracing levels and demonstrate that when many infected individuals bypass treatment, the epidemic can become uncontrollable. When both contact tracing mechanisms operate together, we map out their combined contribution and relative impact on epidemic control. This unified framework yields rigorous and tractable threshold conditions for contact tracing dynamics on networks, extending the applicability of pairwise models beyond the fast-tracing regime and providing new insight into the interplay between disease progression, partial treatment compliance, and higher-order tracing processes.

physics.soc-ph↗

arXiv2025

Disentangling the role of heterogeneity and hyperedge overlap in explosive contagion on higher-order networks

We introduce group-based compartmental modeling (GBCM), a mean-field framework for irreversible contagion in higher-order networks that captures structural heterogeneity and correlations across group sizes. Validated through numerical simulations, GBCM analytically disentangles the role of each interaction order to the global epidemic dynamics, revealing how heterogeneity and inter-order correlations jointly shape the onset of outbreaks and the emergence of explosive dynamics.

physics.soc-ph↗

arXiv2025

Frequency Synchronization Induced by Frequency Detuning

It is widely held that identical systems tend to behave similarly under comparable conditions. Yet, for systems that interact through a network, symmetry breaking can lead to scenarios in which this expectation does not hold. Prominent examples are chimera states in multistable phase-oscillator networks. Here, we show that for a broad class of such networks, asynchronous states can be converted into frequency-synchronized states when identical oscillators are detuned to have different intrinsic frequencies. Importantly, we show that frequency synchronization is achieved over a range of intrinsic frequency detuning and is thus a robust effect. These results, which are supported by theory, simulations, and electrochemical oscillator experiments, reveal a counterintuitive opportunity to use parameter heterogeneity to promote synchronization.

nlin.PS↗

arXiv2025

Inferring contact network characteristics from epidemic data via compact mean-field models

Modelling epidemics using contact networks provides a significant improvement over classical compartmental models by explicitly incorporating the network of contacts. However, while network-based models describe disease spread on a given contact structure, their potential for inferring the underlying network from epidemic data remains largely unexplored. In this work, we consider the edge-based compartmental model (EBCM), a compact and analytically tractable framework, and we integrate it within dynamical survival analysis (DSA) to infer key network properties along with parameters of the epidemic itself. Despite correlations between structural and epidemic parameters, our framework demonstrates robustness in accurately inferring contact network properties from synthetic epidemic simulations. Additionally, we apply the framework to real-world outbreaks, namely the 2001 UK foot-and-mouth disease outbreak and the COVID-19 epidemic in Seoul, to estimate both disease parameters and network characteristics. Our results show that our framework achieves good fits to real-world epidemic data and reliable short-term forecasts. These findings highlight the potential of network-based inference approaches to uncover hidden contact structures, providing insights that can inform the design of targeted interventions and public health strategies.

physics.soc-ph↗

arXiv2025

Inference of noise intensity and phase response from noisy synchronous oscillators

Numerous biological and microscale systems exhibit synchronization in noisy environments. The theory of such noisy oscillators and their synchronization has been developed and experimentally demonstrated, but inferring the noise intensity and phase response is not always straightforward. In this study, we propose a useful formula that enables us to infer the noise intensity and phase response of a noisy oscillator synchronized with periodic external forcing. Through asymptotic approximations for small noise, we show that noisy synchronous oscillators satisfy a simple relationship among the noise intensity and measurable quantities, i.e., the stationary distribution of the oscillation phase and stationary probability current obtained as the average phase velocity, which is verified through systematic numerical analysis. The proposed formula facilitates a unified analysis and design of synchronous oscillators in weakly noisy environments.

nlin.AO↗

arXiv2024

Decoding how higher-order network interactions shape complex contagion dynamics

Complex contagion models that involve contagion along higher-order structures, such as simplicial complexes and hypergraphs, yield new classes of mean-field models. Interestingly, the differential equations arising from many such models often exhibit a similar form, resulting in qualitatively comparable global bifurcation patterns. Motivated by this observation, we investigate a generalized mean-field-type model that provides a unified framework for analysing a range of different models. In particular, we derive analytical conditions for the emergence of different bifurcation regimes exhibited by three models of increasing complexity -- ranging from three- and four-body interactions to two connected populations with both pairwise and three-body interactions. For the first two cases, we give a complete characterisation of all possible outcomes, along with the corresponding conditions on network and epidemic parameters. In the third case, we demonstrate that multistability is possible despite only three-body interactions. Our results reveal that single population models with three-body interactions can only exhibit simple transcritical transitions or bistability, whereas with four-body interactions multistability with two distinct endemic steady states is possible. Surprisingly, the two-population model exhibits multistability via symmetry breaking despite three-body interactions only. Our work sheds light on the relationship between equation structure and model behaviour and makes the first step towards elucidating mechanisms by which different system behaviours arise, and how network and dynamic properties facilitate or hinder outcomes.

physics.soc-ph↗

arXiv2024

A pair-based approximation for simplicial contagion

Higher-order interactions play an important role in complex contagion processes. Mean-field approximations have been used to characterize the onset of spreading in the presence of group interactions. However, individual-based mean-field models are unable to capture correlations between different subsets of nodes, which can significantly influence the dynamics of a contagion process. In this paper, we introduce a pair-based mean-field approximation that allows to study the dynamics of a SIS model on simplicial complexes by taking into account correlations at the level of pairs of nodes. %by taking into account dynamical correlations emerging in groups of nodes. Compared to individual-based mean-field approaches, the proposed approximation yields more accurate predictions of the dynamics of contagion processes on simplicial complexes. Specifically, the pair-based mean-field approximation provides higher accuracy in predicting the extent of the region of bistability, the type of transition from disease-free to endemic state, and the average time evolution of the fraction of infected individuals. Crucially, the pair-based approximation correctly predicts that the onset of the epidemic outbreak in simplicial complexes depends on the strength of higher-order interactions. Overall, our findings highlight the importance of accounting for pair correlations when investigating contagion processes in the presence of higher-order interactions.

physics.soc-ph↗

arXiv2024

Strong coupling yields abrupt synchronization transitions in coupled oscillators

Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling, these transitions can be understood in terms of commonly studied phase approximations. As the coupling strength increases, however, predicting the location and criticality of transition, whether continuous or discontinuous, from the phase dynamics may depend on the order of the phase approximation -- or a phase description of the network dynamics that neglects amplitudes may become impossible altogether. Here we analyze synchronization transitions and their criticality systematically for varying coupling strength in theory and experiments with coupled electrochemical oscillators. First, we analyze bifurcations analysis of synchrony and splay states in an abstract phase model and discuss conditions under which synchronization transitions with different criticalities are possible. Second, we illustrate that transitions with different criticality indeed occur in experimental systems. Third, we highlight that the amplitude dynamics observed in the experiments can be captured in a numerical bifurcation analysis of delay-coupled oscillators. Our results showcase that reduced order phase models may miss important features that one would expect in the dynamics of the full system.

math.DS↗

arXiv2023

Insights from exact social contagion dynamics on networks with higher-order structures

Recently there has been an increasing interest in studying dynamical processes on networks exhibiting higher-order structures, such as simplicial complexes, where the dynamics acts above and beyond dyadic interactions. Using simulations or heuristically derived epidemic spreading models it was shown that new phenomena can emerge, such as bi-stability/multistability. Here, we show that such new emerging phenomena do not require complex contact patterns, such as community structures, but naturally result from the higher-order contagion mechanisms. We show this by deriving an exact higher-order SIS model and its limiting mean-field equivalent for fully connected simplicial complexes. Going beyond previous results, we also give the global bifurcation picture for networks with 3- and 4-body interactions, with the latter allowing for two non-trivial stable endemic steady states. Differently from previous approaches, we are able to study systems featuring interactions of arbitrary order. In addition, we characterise the contributions from higher-order infections to the endemic equilibrium as perturbations of the pairwise baseline, finding that these diminish as the pairwise rate of infection increases. Our approach represents a first step towards a principled understanding of higher-order contagion processes beyond triads and opens up further directions for analytical investigations.

physics.soc-ph↗

arXiv2023

Towards inferring network properties from epidemic data

Epidemic propagation on networks represents an important departure from traditional massaction models. However, the high-dimensionality of the exact models poses a challenge to both mathematical analysis and parameter inference. By using mean-field models, such as the pairwise model (PWM), the complexity becomes tractable. While such models have been used extensively for model analysis, there is limited work in the context of statistical inference. In this paper, we explore the extent to which the PWM with the susceptible-infected-recovered (SIR) epidemic can be used to infer disease- and network-related parameters. The widely-used MLE approach exhibits several issues pertaining to parameter unidentifiability and a lack of robustness to exact knowledge about key quantities such as population size and/or proportion of under reporting. As an alternative, we considered the recently developed dynamical survival analysis (DSA). For scenarios in which there is no model mismatch, such as when data are generated via simulations, both methods perform well despite strong dependence between parameters. However, for real-world data, such as foot-and-mouth, H1N1 and COVID19, the DSA method appears more robust to potential model mismatch and the parameter estimates appear more epidemiologically plausible. Taken together, however, our findings suggest that network-based mean-field models can be used to formulate approximate likelihoods which, coupled with an efficient inference scheme, make it possible to not only learn about the parameters of the disease dynamics but also that of the underlying network.

q-bio.QM↗

arXiv2022

Emergent hypernetworks in weakly coupled oscillators

Networks of weakly coupled oscillators had a profound impact on our understanding of complex systems. Studies on model reconstruction from data have shown prevalent contributions from hypernetworks with triplet and higher interactions among oscillators, in spite that such models were originally defined as oscillator networks with pairwise interactions. Here, we show that hypernetworks can spontaneously emerge even in the presence of pairwise albeit nonlinear coupling given certain triplet frequency resonance conditions. The results are demonstrated in experiments with electrochemical oscillators and in simulations with integrate-and-fire neurons. By developing a comprehensive theory, we uncover the mechanism for emergent hypernetworks by identifying appearing and forbidden frequency resonant conditions. Furthermore, it is shown that microscopic linear (difference) coupling among units results in coupled mean fields, which have sufficient nonlinearity to facilitate hypernetworks. Our findings shed light on the apparent abundance of hypernetworks and provide a constructive way to predict and engineer their emergence.

math.DS↗

arXiv2021

Random heterogeneity outperforms design in network synchronization

A widely held assumption on network dynamics is that similar components are more likely to exhibit similar behavior than dissimilar ones and that generic differences among them are necessarily detrimental to synchronization. Here, we show that this assumption does not generally hold in oscillator networks when communication delays are present. We demonstrate, in particular, that random parameter heterogeneity among oscillators can consistently rescue the system from losing synchrony. This finding is supported by electrochemical-oscillator experiments performed on a multi-electrode array network. Remarkably, at intermediate levels of heterogeneity, random mismatches are more effective in promoting synchronization than parameter assignments specifically designed to facilitate identical synchronization. Our results suggest that, rather than being eliminated or ignored, intrinsic disorder in technological and biological systems can be harnessed to help maintain coherence required for function.

nlin.AO↗

arXiv2020

Covid-19 and Flattening the Curve: a Feedback Control Perspective

Many of the control policies that were put into place during the Covid-19 pandemic had a common goal: to flatten the curve of the number of infected people so that its peak remains under a critical threshold. This letter considers the challenge of engineering a strategy that enforces such a goal using control theory. We introduce a simple formulation of the optimal flattening problem, and provide a closed form solution.This is augmented through nonlinear closed loop tracking of the nominal solution, with the aim of ensuring close-to-optimal performance under uncertain conditions. A key contribution ofthis paper is to provide validation of the method with extensive and realistic simulations in a Covid-19 scenario, with particular focus on the case of Codogno - a small city in Northern Italy that has been among the most harshly hit by the pandemic.

eess.SY↗