Bifurcations in synergistic epidemics on random regular graphs

Taraskin, S. N.; Pérez‐Reche, Francisco J.

doi:10.1088/1751-8121/ab1441

Cited by 5 publications

(3 citation statements)

References 46 publications

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“…The role of synergy in contagions has been investigated in synergistic SIS models and susceptible-infected-removed (SIR) models on various networks; lattices, regular random graphs, random graphs, and small-world networks. As Taraskin and Pérez-Reche proved for the synergistic SIS model on the regular random graph [19], the synergistic effect can induce an explosive spreading and the emergence of a hysteresis loop. In the classical SIS model, the infectious disease becomes extinct or persists if the infection rate is lower or higher than a specified epidemic threshold.…”

Section: Introductionmentioning

confidence: 82%

“…Over the past few years, an increasing body of research has considered the synergistic effect in contagion processes [7,[10][11][12][13][14][15][16][17][18][19]. The synergistic effect represents a nonlinear cooperative effect in the transmission between an infected-susceptible pair, that is, infected neighbors around them enhance the transmission rate.…”

Section: Introductionmentioning

confidence: 99%

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Synergistic epidemic spreading in correlated networks

Mizutaka¹,

Mori²,

Hasegawa³

2021

Preprint

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We investigate the effect of degree correlation on a susceptible-infected-susceptible (SIS) model with a nonlinear cooperative effect (synergy) in infectious transmissions. In a mean-field treatment of the synergistic SIS model on a bimodal network with tunable degree correlation, we identify a discontinuous transition that is independent of the degree correlation strength unless the synergy is absent or extremely weak. Regardless of synergy (absent or present), a positive and negative degree correlation in the model reduces and raises the epidemic threshold, respectively. For networks with a strongly positive degree correlation, the mean-field treatment predicts the emergence of two discontinuous jumps in the steady-state infected density. To test the mean-field treatment, we provide approximate master equations of the present model, which accurately describe the synergistic SIS dynamics. We quantitatively confirm all qualitative predictions of the mean-field treatment in numerical evaluations of the approximate master equations.

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Section: Introductionmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Synergistic epidemic spreading in correlated networks

Mizutaka¹,

Mori²,

Hasegawa³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Previous efforts have been done to incorporate the synergistic effect into classical SIS model by taking the cooperative and the reinforcement effects into the transmission (infection) rate [20][21][22][23][24][25][26]. With the improved model, namely, the synergistic SIS model, realistic phenomena in spreading process, such as explosive epidemic transition and hysteresis behavior, can be well captured and explained through computer simulations [24,27,28].…”

Section: Introductionmentioning

confidence: 99%

From heterogeneous network to homogeneous network: the influence of structure on synergistic epidemic spreading

Lin

Yan

Gao

et al. 2023

J. Phys. A: Math. Theor.

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Synergistic epidemic-like spreading phenomena in networked system occur in various forms in nature and human society. The networks’ structure characterized by its structural heterogeneity aﬀects the synergistic spreading process dramatically. It was believed that the synergistic epidemic spreading follows a continuous transition on heterogeneous networks, but an explosive one on homogeneous networks. In this work, we adopt the model that interpolates between homogeneous and heterogeneous networks to generate a series of studied networks. By continuously changing the ratio of homogeneous structure α of the network, we numerically show that the interplay between the spreading transition and the structural heterogeneity of network is much more complicated. Although the explosive epidemic transition is likely to be hindered by structural heterogeneity, it could occur on completely heterogeneous network as long as the synergistic strength is suﬃciently strong. The predictions of heterogeneous mean-ﬁeld analysis agree with the numerical results, thus helping to understand the role of structural heterogeneity in aﬀecting synergistic epidemic spreading.

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Investigation on the influence of heterogeneous synergy in contagion processes on complex networks

Yan

Gao

Wang

et al. 2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Synergistic contagion in a networked system occurs in various forms in nature and human society. While the influence of network’s structural heterogeneity on synergistic contagion has been well studied, the impact of individual-based heterogeneity on synergistic contagion remains unclear. In this work, we introduce individual-based heterogeneity with a power-law form into the synergistic susceptible–infected–susceptible model by assuming the synergistic strength as a function of individuals’ degree and investigate this synergistic contagion process on complex networks. By employing the heterogeneous mean-field (HMF) approximation, we analytically show that the heterogeneous synergy significantly changes the critical threshold of synergistic strength σc that is required for the occurrence of discontinuous phase transitions of contagion processes. Comparing to the synergy without individual-based heterogeneity, the value of σc decreases with degree-enhanced synergy and increases with degree-suppressed synergy, which agrees well with Monte Carlo prediction. Next, we compare our heterogeneous synergistic contagion model with the simplicial contagion model [Iacopini et al., Nat. Commun. 10, 2485 (2019)], in which high-order interactions are introduced to describe complex contagion. Similarity of these two models are shown both analytically and numerically, confirming the ability of our model to statistically describe the simplest high-order interaction within HMF approximation.

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Bifurcations in synergistic epidemics on random regular graphs

Cited by 5 publications

References 46 publications

Synergistic epidemic spreading in correlated networks

Synergistic epidemic spreading in correlated networks

From heterogeneous network to homogeneous network: the influence of structure on synergistic epidemic spreading

Investigation on the influence of heterogeneous synergy in contagion processes on complex networks

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