Hathcock D, Strogatz SH. Asymptotic Absorption-Time Distributions in Extinction-Prone Markov Processes.
PHYSICAL REVIEW LETTERS 2022;
128:218301. [PMID:
35687454 DOI:
10.1103/physrevlett.128.218301]
[Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Revised: 03/27/2022] [Accepted: 04/14/2022] [Indexed: 06/15/2023]
Abstract
We characterize absorption-time distributions for birth-death Markov chains with an absorbing boundary. For "extinction-prone" chains (which drift on average toward the absorbing state) the asymptotic distribution is Gaussian, Gumbel, or belongs to a family of skewed distributions. The latter two cases arise when the dynamics slow down dramatically near the boundary. Several models of evolution, epidemics, and chemical reactions fall into these classes; in each case we establish new results for the absorption-time distribution. Applications to African sleeping sickness are discussed.
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