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• W2950605817 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." @default.
• W2950605817 created "2019-06-27" @default.
• W2950605817 creator A5024863178 @default.
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• W2950605817 date "2017-07-13" @default.
• W2950605817 modified "2023-10-13" @default.
• W2950605817 title "Takeover times for a simple model of network infection" @default.
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• W2950605817 doi "https://doi.org/10.1103/physreve.96.012313" @default.
• W2950605817 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/7217517" @default.
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