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This paper is dedicated to the study of the interaction between dynamical systems and percolation models, with views towards the study of viral infections whose virus mutate with time. Recall that r-bootstrap percolation describes a deterministic process where vertices of a graph are infected once r neighbors of it are infected. We generalize this by introducing F(t)-bootstrap percolation, a time-dependent process where the number of neighbouring vertices which need to be infected for a disease to be transmitted is determined by a percolation function F(t) at each time t. After studying some of the basic properties of the model, we consider smallest percolating sets and construct a polynomial-timed algorithm to nd one smallest minimal percolating set on nite trees for certain F(t)-bootstrap percolation models.
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A trust model for spreading gossip in social networks: a multi-type bootstrap percolation model
We introduce here a multi-type bootstrap percolation model, which we call T -Bootstrap Percolation ( T -BP), and apply it to study information propagation in social networks. In this model, a social network is represented by a graph G whose vertices have different labels corresponding to the type of role the person plays in the network (e.g. a student, an educator etc.). Once an initial set of vertices of G is randomly selected to be carrying a gossip (e.g. to be infected), the gossip propagates to a new vertex provided it is transmitted by a minimum threshold of vertices with different labels. By considering random graphs, which have been shown to closely represent social networks, we study different properties of the T -BP model through numerical simulations, and describe its implications when applied to rumour spread, fake news and marketing strategies.
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- PAR ID:
- 10232951
- Date Published:
- Journal Name:
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 476
- Issue:
- 2235
- ISSN:
- 1364-5021
- Page Range / eLocation ID:
- 20190826
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rspa.2019.0826
