Disease spreading with social distancing: A prevention strategy in disordered multiplex networks.

The frequent emergence of diseases with the potential to become threats at local and global scales, such as influenza A(H1N1), SARS, MERS, and recently COVID-19 disease, makes it crucial to keep designing models of disease propagation and strategies to prevent or mitigate their effects in populations. Since isolated systems are exceptionally rare to find in any context, especially in human contact networks, here we examine the susceptible-infected-recovered model of disease spreading in a multiplex network formed by two distinct networks or layers, interconnected through a fraction q of shared individuals (overlap). We model the interactions through weighted networks, because person-to-person interactions are diverse (or disordered); weights represent the contact times of the interactions.

Ring vaccination strategy in networks: A mixed percolation approach.

Ring vaccination is a mitigation strategy that consists in seeking and vaccinating the contacts of a sick patient, in order to provide immunization and halt the spread of disease. We study an extension of the susceptible-infected-recovered (SIR) epidemic model with ring vaccination in complex and spatial networks. Previously, a correspondence between this model and a link percolation process has been established, however, this is only valid in complex networks.

Reversible bootstrap percolation: Fake news and fact checking.

Bootstrap percolation has been used to describe opinion formation in society and other social and natural phenomena. The formal equation of the bootstrap percolation may have more than one solution, corresponding to several stable fixed points of the corresponding iteration process. We construct a reversible bootstrap percolation process, which converges to these extra solutions displaying a hysteresis typical of discontinuous phase transitions.

Insights into bootstrap percolation: Its equivalence with k-core percolation and the giant component.

K-core and bootstrap percolation are widely studied models that have been used to represent and understand diverse deactivation and activation processes in natural and social systems. Since these models are considerably similar, it has been suggested in recent years that they could be complementary. In this manuscript we provide a rigorous analysis that shows that for any degree and threshold distributions heterogeneous bootstrap percolation can be mapped into heterogeneous k-core percolation and vice versa, if the functionality thresholds in both processes satisfy a complementary relation.