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### An overview of epidemic models with phase transitions to absorbing states running on top of complex networks

**Por:** Angélica S. Mata

**Autor contato:** Angélica S. Mata

**Resumo**

Dynamical systems running on the top of complex networks have been extensively investigated for decades. But this topic still remains among the most relevant issues in complex network theory due to its range of applicability. The contact process (CP) and the susceptible–infected–susceptible (SIS) model are used quite often to describe epidemic dynamics. Despite their simplicity, these models are robust to predict the kernel of real situations. In this work, we review concisely both processes that are well-known and very applied examples of models that exhibit absorbing-state phase transitions. In the epidemic scenario, individuals can be infected or susceptible. A phase transition between a disease-free (absorbing) state and an active stationary phase (where a fraction of the population is infected) are separated by an epidemic threshold. For the SIS model, the central issue is to determine this epidemic threshold on heterogeneous networks. For the CP model, the main interest is to relate critical exponents with statistical properties of the network.

**Publicado em:** Chaos: An Interdisciplinary Journal of Nonlinear Science (2020)

**Artigo completo:** https://doi.org/10.1063/5.0033130

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

**Por:** Wesley Cota; Angélica S. Mata; Silvio C. Ferreira

**Autor contato:** Angélica S. Mata

**Resumo**

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.

**Publicado em:** Physical Review E (2018)

**Artigo completo:** https://doi.org/10.1103/PhysRevE.98.012310