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Title: Estimating the expected time to population extinction with semi-stochastic models

Authors: B.J. Cairns.

Reference: Mathematical Population Studies 16(3): 199-220.

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"Semi-stochastic" or "piecewise-deterministic" Markov processes generalize continuous-time Markov chains, allowing for deterministic flow between Markovian jumps. They have been employed as models for the effect of environmental catastrophes on biological populations, for the progress of infectious diseases within and between hosts, and for the management of fisheries. One application is to solve first-exit time problems, which include calculations of the expected time or of the expected value from the present to extinction of processes with state-dependent rewards or costs. A simple and robust numerical method gives the solution of first-exit time problems for a wide range of semi-stochastic processes.

Keywords. Extinction, first-exit time, piecewise-deterministic, population process, semi-stochastic, state-dependent.

Acknowledgement. The author would like to thank Phil Pollett, Hugh Possingham and two anonymous thesis examiners for their comments on an earlier version of this work. Financial support was provided by a PhD scholarship from the Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems while the author was a PhD candidate in the School of Physical Sciences, University of Queensland, and by the BBSRC and UK Food Standards Agency.

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Cancer Epidemiology Unit, University of Oxford, Richard Doll Building, Roosevelt Drive, Oxford OX3 7LF, U.K.