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On the time to extinction in recurrent epidemics
Author(s) -
Nåsell I.
Publication year - 1999
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00178
Subject(s) - extinction (optical mineralogy) , statistical physics , persistence (discontinuity) , mathematics , stationary distribution , magnitude (astronomy) , econometrics , physics , statistics , geology , astrophysics , optics , markov chain , geotechnical engineering
An approximation is derived for the expected time to extinction in a stochastic model for recurrent epidemics. Numerical illustrations indicate that the approximation is crude but that it has the correct order of magnitude. The quasi‐stationary distribution plays an important role in the derivation. Approximations for the critical community size and of the persistence threshold are derived. Comments are made on the classical study by Bartlell (1956–1960).