arXiv subjects

Wesley Cota

Publications and source records attributed to Wesley Cota.

13 recordsLinked to original sources

arXiv2026

Epidemic spreading on multigraphs

Multigraphs are graphs in which multiple links between pairs of nodes are allowed, whereas they are forbidden in simple graphs, the latter being widely used in network science. Simple graphs generated by the configuration model have served as a benchmark for validating theoretical approaches to dynamical processes on networks. However, generating large scale-free networks with degree exponent $\gamma<3$ introduces uncontrolled disassortative correlations and severe computational limitations due to the prohibition of reconnecting hubs. These constraints do not exist in multigraphs. We investigate how multiple connections affect epidemic spreading by comparing several epidemic models exhibiting an active steady state on simple graphs and multigraphs sharing the same degree sequence and natural upper cutoff. By analyzing epidemic thresholds, finite-size scaling, and localization, we show that differences between simple graphs and multigraphs emerge only when epidemic activity can persist on isolated hubs (star subgraphs) for times exponentially long in the hub degree. Our results remove a methodological barrier to the study of dynamical processes on large scale-free networks.

physics.soc-ph↗

arXiv2025

Impacts of bridging nodes on the epidemic activation mechanisms

Bridging nodes, which connect critical components of a network, play an important role in maintaining structural integrity and facilitating communication within the network, representing indirect yet relevant connections. Epidemic triggering mechanisms in networks often involve long-range mutual activation of hubs, mediated by paths composed of low-degree nodes. While low-degree nodes are abundant in networks, their role in bridging central nodes in epidemic activation mechanisms has not been thoroughly analyzed. Starting with a backbone network with a power-law degree distribution, we investigate the role of adding degree-2 bridging nodes that are preferentially attached to hubs. Our findings reveal that bridging nodes can mediate an indirect feedback interaction between hubs that modifies the epidemic localization and activation mechanisms of the epidemic processes with recurrent infections. In particular, the collective activation observed in the presence of waning immunity, which produces a finite epidemic threshold in power-law networks with degree exponent $\gamma>3$, is altered to a localized activation with a vanishing threshold. Our numerical results are analytically supported by the non-backtracking matrix properties that emerge in the recurrent dynamical message-passing theory.

physics.soc-ph↗

arXiv2025

Efficient Gillespie algorithms for spreading phenomena in large and heterogeneous higher-order networks

Higher-order interactions, where groups of nodes interact collectively rather than pairwisely, are central to many complex systems, from neural and ecological networks to social contagion. However, simulating dynamical processes on such higher-order structures remains computationally challenging due to the combinatorial growth of possible interactions. Here, we develop efficient and statistically exact Gillespie algorithms for Markovian spreading dynamics on large and heterogeneous hypergraphs. By incorporating phantom processes $-$events that advance time without altering the system's state$-$, we drastically reduce the computational complexity of standard algorithms ($\mathcal{O}(N^2)$), achieving up to linear scaling with system size. Relying on the susceptible-infected-susceptible model with critical mass thresholds as a benchmark, we show that the optimized algorithms outperform standard approaches by several orders of magnitude, enabling simulations of networks with millions of nodes and broad heterogeneity in both degree and interaction order. Efficient sampling methods, needed to overcome the bottlenecks imposed by either a high maximum order or number of interactions, and other dynamical processes on higher-order networks are tackled. These results establish a general framework for scalable, continuous-time simulations of higher-order contagion and related dynamical processes.

physics.soc-ph↗

arXiv2022

Data-driven approach in a compartmental epidemic model to assess undocumented infections

Nowcasting and forecasting of epidemic spreading rely on incidence series of reported cases to derive the fundamental epidemiological parameters for a given pathogen. Two relevant drawbacks for predictions are the unknown fractions of undocumented cases and levels of nonpharmacological interventions, which span highly heterogeneously across different places and times. We describe a simple data-driven approach using a compartmental model including asymptomatic and presymptomatic contagions that allows to estimate both the level of undocumented infections and the value of effective reproductive number R t from time series of reported cases, deaths, and epidemiological parameters. The method was applied to epidemic series for COVID-19 across different municipalities in Brazil allowing to estimate the heterogeneity level of under-reporting across different places. The reproductive number derived within the current framework is little sensitive to both diagnosis and infection rates during the asymptomatic states. The methods described here can be extended to more general cases if data is available and adapted to other epidemiological approaches and surveillance data.

q-bio.PE↗

arXiv2022

Effects of infection fatality ratio and social contact matrices on vaccine prioritization strategies

Effective strategies of vaccine prioritization are essential to mitigate the impacts of severe infectious diseases. We investigate the role of infection fatality ratio (IFR) and social contact matrices on vaccination prioritization using a compartmental epidemic model fueled by real-world data of different diseases and countries. Our study confirms that massive and early vaccination is extremely effective to reduce the disease fatality if the contagion is mitigated, but the effectiveness is increasingly reduced as vaccination beginning delays in an uncontrolled epidemiological scenario. The optimal and least effective prioritization strategies depend non-linearly on epidemiological variables. Regions of the epidemiological parameter space, in which prioritizing the most vulnerable population is more effective than the most contagious individuals, depend strongly on the IFR age profile being, for example, substantially broader for COVID-19 in comparison with seasonal influenza. Demographics and social contact matrices deform the phase diagrams but do not alter their qualitative shapes.

q-bio.PE↗

arXiv2021

Infectious disease dynamics in metapopulations with heterogeneous transmission and recurrent mobility

Human mobility, contact patterns, and their interplay are key aspects of our social behavior that shape the spread of infectious diseases across different regions. In the light of new evidence and data sets about these two elements, epidemic models should be refined to incorporate both the heterogeneity of human contacts and the complexity of mobility patterns. Here, we propose a theoretical framework that allows accommodating these two aspects in the form of a set of Markovian equations. We validate these equations with extensive mechanistic simulations and derive analytically the epidemic threshold. The expression of this critical value allows us to evaluate its dependence on the specific demographic distribution, the structure of mobility flows, and the heterogeneity of contact patterns, thus shedding light on the microscopic mechanisms responsible for the epidemic detriment driven by recurrent mobility patterns reported in the literature.

physics.soc-ph↗

arXiv2020

Outbreak diversity in epidemic waves propagating through distinct geographical scales

A central feature of an emerging infectious disease in a pandemic scenario is the spread through geographical scales and the impacts on different locations according to the adopted mitigation protocols. We investigated a stochastic epidemic model with the metapopulation approach in which patches represent municipalities. Contagion follows a stochastic compartmental model for municipalities; the latter, in turn, interact with each other through recurrent mobility. As a case of study, we consider the epidemic of COVID-19 in Brazil performing data-driven simulations. Properties of the simulated epidemic curves have very broad distributions across different geographical locations and scales, from states, passing through intermediate and immediate regions down to municipality levels. Correlations between delay of the epidemic outbreak and distance from the respective capital cities were predicted to be strong in several states and weak in others, signaling influences of multiple epidemic foci propagating towards the inland cities. Responses of different regions to a same mitigation protocol can vary enormously implying that the policies of combating the epidemics must be engineered according to the region' specificity but integrated with the overall situation. Real series of reported cases confirm the qualitative scenarios predicted in simulations. Even though we restricted our study to Brazil, the prospects and model can be extended to other geographical organizations with heterogeneous demographic distributions.

physics.soc-ph↗

arXiv2019

Quantifying echo chamber effects in information spreading over political communication networks

Echo chambers in online social networks, in which users prefer to interact only with ideologically-aligned peers, are believed to facilitate misinformation spreading and contribute to radicalize political discourse. In this paper, we gauge the effects of echo chambers in information spreading phenomena over political communication networks. Mining 12 million Twitter messages, we reconstruct a network in which users interchange opinions related to the impeachment of the former Brazilian President Dilma Rousseff. We define a continuous {political position} parameter, independent of the network's structure, that allows to quantify the presence of echo chambers in the strongly connected component of the network, reflected in two well-separated communities of similar sizes with opposite views of the impeachment process. By means of simple spreading models, we show that the capability of users in propagating the content they produce, measured by the associated spreadability, strongly depends on their attitude. Users expressing pro-impeachment sentiments are capable to transmit information, on average, to a larger audience than users expressing anti-impeachment sentiments. Furthermore, the users' spreadability is correlated to the diversity, in terms of political position, of the audience reached. Our method can be exploited to identify the presence of echo chambers and their effects across different contexts and shed light upon the mechanisms allowing to break echo chambers.

physics.soc-ph↗

arXiv2019

Spectral properties and the accuracy of mean-field approaches for epidemics on correlated networks

We present a comparison between stochastic simulations and mean-field theories for the epidemic threshold of the susceptible-infected-susceptible (SIS) model on correlated networks (both assortative and disassortative) with power-law degree distribution $P(k)\sim k^{-γ}$. We confirm the vanishing of the threshold regardless of the correlation pattern and the degree exponent $γ$. Thresholds determined numerically are compared with quenched mean-field (QMF) and pair quenched mean-field (PQMF) theories. Correlations do not change the overall picture: QMF and PQMF provide estimates that are asymptotically correct for large size for $γ<5/2$, while they only capture the vanishing of the threshold for $γ>5/2$, failing to reproduce quantitatively how this occurs. For a given size, PQMF is more accurate. We relate the variations in the accuracy of QMF and PQMF predictions with changes in the spectral properties (spectral gap and localization) of standard and modified adjacency matrices, which rule the epidemic prevalence near the transition point, depending on the theoretical framework. We also show that, for $γ<5/2$, while QMF provides an estimate of the epidemic threshold that is asymptotically exact, it fails to reproduce the singularity of the prevalence around the transition.

physics.soc-ph↗

arXiv2018

Robustness and fragility of the susceptible-infected-susceptible epidemic models on complex networks

We analyze two alterations of the standard susceptible-infected-susceptible (SIS) dynamics that preserve the central properties of spontaneous healing and infection capacity of a vertex increasing unlimitedly with its degree. All models have the same epidemic thresholds in mean-field theories but depending on the network properties, simulations yield a dual scenario, in which the epidemic thresholds of the modified SIS models can be either dramatically altered or remain unchanged in comparison with the standard dynamics. For uncorrelated synthetic networks having a power-law degree distribution with exponent $γ<5/2$, the SIS dynamics are robust exhibiting essentially the same outcomes for all investigated models. A threshold in better agreement with the heterogeneous rather than quenched mean-field theory is observed in the modified dynamics for exponent $γ>5/2$. Differences are more remarkable for $γ>3$ where a finite threshold is found in the modified models in contrast with the vanishing threshold of the original one. This duality is elucidated in terms of epidemic lifespan on star graphs. We verify that the activation of the modified SIS models is triggered in the innermost component of the network given by a $k$-core decomposition for $γ<3$ while it happens only for $γ<5/2$ in the standard model. For $γ>3$, the activation in the modified dynamics is collective involving essentially the whole network while it is triggered by hubs in the standard SIS. The duality also appears in the finite-size scaling of the critical quantities where mean-field behaviors are observed for the modified, but not for the original dynamics. Our results feed the discussions about the most proper conceptions of epidemic models to describe real systems and the choices of the most suitable theoretical approaches to deal with these models.

physics.soc-ph↗

arXiv2018

Griffiths phases in infinite-dimensional, non-hierarchical modular networks

Griffiths phases (GPs), generated by the heterogeneities on modular networks, have recently been suggested to provide a mechanism, rid of fine parameter tuning, to explain the critical behavior of complex systems. One conjectured requirement for systems with modular structures was that the network of modules must be hierarchically organized and possess finite dimension. We investigate the dynamical behavior of an activity spreading model, evolving on heterogeneous random networks with highly modular structure and organized non-hierarchically. We observe that loosely coupled modules act as effective rare-regions, slowing down the extinction of activation. As a consequence, we find extended control parameter regions with continuously changing dynamical exponents for single network realizations, preserved after finite size analyses, as in a real GP. The avalanche size distributions of spreading events exhibit robust power-law tails. Our findings relax the requirement of hierarchical organization of the modular structure, which can help to rationalize the criticality of modular systems in the framework of GPs.

physics.soc-ph↗

arXiv2017

Optimized Gillespie algorithms for the simulation of Markovian epidemic processes on large and heterogeneous networks

Numerical simulation of continuous-time Markovian processes is an essential and widely applied tool in the investigation of epidemic spreading on complex networks. Due to the high heterogeneity of the connectivity structure through which epidemics is transmitted, efficient and accurate implementations of generic epidemic processes are not trivial and deviations from statistically exact prescriptions can lead to uncontrolled biases. Based on the Gillespie algorithm (GA), in which only steps that change the state are considered, we develop numerical recipes and describe their computer implementations for statistically exact and computationally efficient simulations of generic Markovian epidemic processes aiming at highly heterogeneous and large networks. The central point of the recipes investigated here is to include phantom processes, that do not change the states but do count for time increments. We compare the efficiencies for the susceptible-infected-susceptible, contact process and susceptible-infected-recovered models, that are particular cases of a generic model considered here. We numerically confirm that the simulation outcomes of the optimized algorithms are statistically indistinguishable from the original GA and can be several orders of magnitude more efficient.

physics.soc-ph↗

arXiv2016

Griffiths effects of the susceptible-infected-susceptible epidemic model on random power-law networks

We provide numerical evidence for slow dynamics of the susceptible-infected-susceptible model evolving on finite-size random networks with power-law degree distributions. Extensive simulations were done by averaging the activity density over many realizations of networks. We investigated the effects of outliers in both highly fluctuating (natural cutoff) and non-fluctuating (hard cutoff) most connected vertices. Logarithmic and power-law decays in time were found for natural and hard cutoffs, respectively. This happens in extended regions of the control parameter space $λ_1<λ<λ_2$, suggesting Griffiths effects, induced by the topological inhomogeneities. Optimal fluctuation theory considering sample-to-sample fluctuations of the pseudo thresholds is presented to explain the observed slow dynamics. A quasistationary analysis shows that response functions remain bounded at $λ_2$. We argue these to be signals of a smeared transition. However, in the thermodynamic limit the Griffiths effects loose their relevancy and have a conventional critical point at $λ_c=0$. Since many real networks are composed by heterogeneous and weakly connected modules, the slow dynamics found in our analysis of independent and finite networks can play an important role for the deeper understanding of such systems.

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