On linear birth-and-death processes in a random environment | Zendy

Nicolas Bacaër | Zendy; Abdelkarim Ed-Darraz | Zendy

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On linear birth-and-death processes in a random environment

Author(s) -

Nicolas Bacaër,

Abdelkarim Ed-Darraz

Publication year - 2013

Publication title -

journal of mathematical biology

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.928

H-Index - 97

eISSN - 1432-1416

pISSN - 0303-6812

DOI - 10.1007/s00285-013-0696-0

Subject(s) - extinction probability , birth–death process , extinction (optical mineralogy) , mathematics , type (biology) , markov process , statistics , biology , demography , ecology , sociology , paleontology , population , population size

We study the probability of extinction for single-type and multi-type continuous-time linear birth-and-death processes in a finite Markovian environment. The probability of extinction is equal to 1 almost surely if and only if the basic reproduction number R(0) is ≤ 1, the key point being to identify a suitable definition of R(0) for such a result to hold.

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