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

Wesley Cota, Angélica S. Mata, and Silvio C. Ferreira
Phys. Rev. E 98, 012310 – Published 18 July 2018

Abstract

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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  • Received 23 April 2018

DOI:https://doi.org/10.1103/PhysRevE.98.012310

©2018 American Physical Society

Physics Subject Headings (PhySH)

NetworksInterdisciplinary PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Wesley Cota1, Angélica S. Mata2, and Silvio C. Ferreira1,3

  • 1Departamento de Física, Universidade Federal de Viçosa, 36570-900 Viçosa, Minas Gerais, Brazil
  • 2Departamento de Física, Universidade Federal de Lavras, 37200-000 Lavras, Minas Gerais, Brazil
  • 3National Institute of Science and Technology for Complex Systems, Brazil

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Issue

Vol. 98, Iss. 1 — July 2018

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