Simplicial SIRS epidemic models with nonlinear incidence rates

Wang, Dong; Zhao, Yi; Luo, Jianfeng; Hui, Leng

doi:10.1063/5.0040518

Cited by 44 publications

(7 citation statements)

References 66 publications

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“…The results indicate that the pattern formation under the multiplex network seems not require a large difference in the diffusion rate compared with the single-layer network may exist [53]. Recently, the higher-order structure of networks has received much attention [55][56][57][58], and some works of Turing pattern on networks with higher-order structures have appeared [58,59]. They find that the specific parameter regions of Turing Pattern formation in reaction-diffusion information propagation model on multiplex simplicial complexes pattern exist only under the high-order interaction, which indicates that the high-order structure plays a key role in pattern formation.…”

Section: Introductionmentioning

confidence: 94%

Pattern formation in reaction-diffusion information propagation model on multiplex simplicial complexes

Zhou

Zhao

2023

Preprint

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Turing pattern for explaining the spatial distribution in nature mostly focused on continuous media and existing networks but there are few attempts at studying them on the systems with high-order interactions. Considering that high-order interactions have a particularly significant impact on rumor propagation, this article establishes a generalized reaction-diffusion rumor propagation model based on a multiplex network, where simplicial complexes are employed to describe the high-order structures. It aims to provide the spatial distribution patterns of the population participating in rumor propagation and identify structural factors that affect such patterns. We theoretically give the necessary conditions for Turing instability in the single-layer and multiplex networks with consideration of high-order interactions. In the numerical simulation, we demonstrate that Turing pattern is controlled by adjusting the diffusion coefficient, high-order structure intensity, and average degree of the network. The results conclude that: (i) in a single-layer network, Turing pattern only exists when high-order interactions appear, and the difference in diffusion rate plays a decisive role, (ii) in a multiplex network, Turing pattern can still be observed under the same diffusion rates, which are affected by the difference of higher-order intensity between two layers, and (iii) in the existing networks, the average degree of the network takes an important impact on Turing pattern. All these findings contribute to comprehending the impact of network structure on pattern formation, especially the high-order interactions on Turing pattern.

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Section: Introductionmentioning

confidence: 94%

Pattern formation in reaction-diffusion information propagation model on multiplex simplicial complexes

Zhou

Zhao

2023

Preprint

Self Cite

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“…To account for more realistic situation, some mechanisms such as the nonlinear infection [36] should be considered. Besides, with much attention on the dynamical behaviors induced by the synergy and the higher order contagion mechanism [15,[37][38][39][40], including explosive spreading and the emergence of multi-stable region, there are much less efforts attempting to focus on the structural impacts on synergistic spreading. Thus, further work could focus on the effects of other topological characteristics which exist in real networks widely, e.g.…”

Section: Conclusion and Discussionmentioning

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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“…Apart from the heterogeneity of individual activity levels, the heterogeneity of network topology is critical in the complex propagation process. Information diffusion usually involves higher-order interactions, whereas epidemic transmission prefers pairwise interactions [33][34][35][36][37]. In recent years, the study on the interaction between information diffusion and epidemic transmission under higher-order role has become a hot research topic, which has attracted extensive attention from researchers in various disciplines [38][39][40].…”

Section: Introductionmentioning

confidence: 99%

The interaction of information diffusion and epidemic transmission in time-varying multiplex networks with simplicial complexes and asymmetric activity levels

Xie,

Huo,

Dong

et al. 2024

Phys. Scr.

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Information diffusion among individuals occurs in various ways, mainly involving pairwise and higher-order interactions, and their coexistence can be characterized by simplicial complexes. This paper introduces a novel two-layer model that investigates coupled information-epidemic propagation. Specifically, the upper layer represents the virtual layer that depicts information diffusion, where the interaction process among individuals is not only limited to pairwise interactions but also influenced by higher-order interactions. The lower layer denotes the physical contact layer to portray epidemic transmission, where the interaction process among individuals is only considered in pairwise interactions. In particular, the emergence of asymmetric activity levels in two-layer networks reshapes the propagation mechanism. We then employ the micro-Marko chain approach (MMCA) to establish the probabilistic transfer equation for each state, deduce the epidemic outbreak threshold, and investigate the equilibrium and stability of the proposed model. Furthermore, we perform extensive Monte Carlo (MC) simulations to validate the theoretical predictions. The results demonstrate that the higher-order interaction generates synergistic reinforcement mechanisms that both facilitate information diffusion and inhibit epidemic transmission. Moreover, this study suggests that the activity level of individuals at the physical contact level has a greater impact on epidemic transmission. In addition, we utilize two different networks to explore the influence of network structural features on the transmission and scale of epidemics.

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Simplicial SIRS epidemic models with nonlinear incidence rates

Cited by 44 publications

References 66 publications

Pattern formation in reaction-diffusion information propagation model on multiplex simplicial complexes

Pattern formation in reaction-diffusion information propagation model on multiplex simplicial complexes

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

The interaction of information diffusion and epidemic transmission in time-varying multiplex networks with simplicial complexes and asymmetric activity levels

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