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Math Biosci. 2006 Aug;202(2):310-22. Epub 2006 Apr 19.

Extinction times for a birth-death process with two phases.

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1
Department of Mathematics, University of Queensland, QLD 4072, Australia. jvr@maths.uq.edu.au <jvr@maths.uq.edu.au>

Abstract

Many populations have a negative impact on their habitat or upon other species in the environment if their numbers become too large. For this reason they are often subjected to some form of control. One common control regime is the reduction regime: when the population reaches a certain threshold it is controlled (for example culled) until it falls below a lower predefined level. The natural model for such a controlled population is a birth-death process with two phases, the phase determining which of two distinct sets of birth and death rates governs the process. We present formulae for the probability of extinction and the expected time to extinction, and discuss several applications.

PMID:
16624337
DOI:
10.1016/j.mbs.2006.02.004
[Indexed for MEDLINE]
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