ArticlePhysical review. E2017
Takeover times for a simple model of network infection.
Article in Physical review. E, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 7 papers.
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Who cites it
7 citing papers in PubMed.
- Spectral dynamics of guided edge removals and identifying transient amplifiers for death-Birth updating.Journal of mathematical biology · 2023Article
- Suppressors of fixation can increase average fitness beyond amplifiers of selection.Proceedings of the National Academy of Sciences of the United States of America · 2022Article
- Fixation probabilities in network structured meta-populations.Scientific reports · 2021Article
- Spectral analysis of transient amplifiers for death-birth updating constructed from regular graphs.Journal of mathematical biology · 2021Article
- Computation and Simulation of Evolutionary Game Dynamics in Finite Populations.Scientific reports · 2019Article
- Timing Information Propagation in Interactive Networks.Scientific reports · 2019Article
- Evolutionary dynamics of incubation periods.eLife · 2017Article
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Authors and funding
3 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
We study a stochastic model of infection spreading on a network. At each time step a node is chosen at random, along with one of its neighbors. If the node is infected and the neighbor is susceptible, the neighbor becomes infected. How many time steps T does it take to completely infect a network of N nodes, starting from a single infected node? An analogy to the classic "coupon collector" problem of probability theory reveals that the takeover time T is dominated by extremal behavior, either when there are only a few infected nodes near the start of the process or a few susceptible nodes near the end. We show that for N≫1, the takeover time T is distributed as a Gumbel distribution for the star graph, as the convolution of two Gumbel distributions for a complete graph and an Erdős-Rényi random graph, as a normal for a one-dimensional ring and a two-dimensional lattice, and as a family of intermediate skewed distributions for d-dimensional lattices with d≥3 (these distributions approach the convolution of two Gumbel distributions as d approaches infinity). Connections to evolutionary dynamics, cancer, incubation periods of infectious diseases, first-passage percolation, and other spreading phenomena in biology and physics are discussed.
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