Collective versus hub activation of epidemic phases on networks

Ferreira, Silvio C.; Sander, Renan S.; Pastor-Satorras, Romualdo

doi:10.1103/physreve.93.032314

Cited by 51 publications

(90 citation statements)

References 42 publications

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“…Our results gathered with previous reports of Ref. [12], in which waning immunity can drastically change the threshold behavior, lead to the following take-home messages. Firstly, the metastable, localized, and active states of the standard SIS dynamics necessary to sustain the endemic activity for any infection rate for γ > 3 are not universal and their realizations in real epidemic processes may be unrealistic.…”

Section: Introductionsupporting

confidence: 86%

“…In Ref. [12], this criterion notably predicted that waning immunity [29], in which infected individuals are temporarily immunized before to become susceptible, leads to a finite threshold for γ > 3 which disagrees with the prediction of QMF approximation, but in agreement with extensive numerical simulations.…”

Section: Introductionmentioning

confidence: 87%

“…power-law degree distributions [12]. The criterion involves the recovering time τ k of an epidemics on a star graph, consisting of a central vertex connected to k leaves of degree 1 that mimics the hubs of a network, and the time τ (inf) that the hubs take to mutually transmit the infection to each other.…”

Section: Introductionmentioning

confidence: 99%

“…For 2 < γ < 5/2, the SIS infection mechanism is robust and all models have essentially the same epidemic threshold. This duality is explained in terms of epidemic activation mechanisms [9,12,32].…”

Section: Introductionmentioning

confidence: 99%

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

2018

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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.

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Section: Introductionsupporting

confidence: 86%

Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2018

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“…Compared to the uncorrelated case, assortative networks (α > 0) have a smaller threshold, while the threshold is larger for α < 0, i.e., disassortative mixing, in agreement with the behavior of the LEV of the adjacency matrix [14,23]. In the case γ > 3, this phenomenology can be qualitatively explained by considering the mechanism of long-range mutual reinfection of hubs [25,45,47], which triggers the epidemic transition. According to this mechanism, the subgraph consisting of the hub plus its nearest-neighbors can sustain in isolation an active state for times long enough to permit the activation of other hubs, even if they are not directly connected.…”

Section: Resultssupporting

confidence: 65%

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

Silva

Ferreira

Cota

et al. 2019

Phys. Rev. Research

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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) ∼ 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.

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Modeling Communicable Diseases, Human Mobility, and Epidemics: A Review

et al. 2022

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The spatiotemporal propagation patterns of recent infectious diseases, originated as localized epidemic outbreaks and eventually becoming global pandemics, are highly influenced by human mobility. Case exportation from endemic areas to the rest of the countries has become unavoidable because of the striking growth of the global mobility network, helping to overcome the physical distance existing between faraway regions. In this context, understanding the features driving contagions upon the arrival of an index case in local environments constitutes an essential task to devise policies aimed at avoiding the community transmission of these diseases and the subsequent case exportation to other unaffected areas. In this review, an overview of the different models addressing this topic is given, focusing on the movement-interaction-return model and different subsequent frameworks introduced to explain the complex interplay between the recurrent movements and contagion dynamics.

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Collective versus hub activation of epidemic phases on networks

Cited by 51 publications

References 42 publications

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

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

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

Modeling Communicable Diseases, Human Mobility, and Epidemics: A Review

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