Fast Variables in Stochastic Population Dynamics

Nonfiction, Science & Nature, Science, Other Sciences, System Theory, Biological Sciences, Ecology, Social & Cultural Studies, Social Science
Cover of the book Fast Variables in Stochastic Population Dynamics by George William Albert Constable, Springer International Publishing
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Author: George William Albert Constable ISBN: 9783319212180
Publisher: Springer International Publishing Publication: July 25, 2015
Imprint: Springer Language: English
Author: George William Albert Constable
ISBN: 9783319212180
Publisher: Springer International Publishing
Publication: July 25, 2015
Imprint: Springer
Language: English

 In this thesis two variants of the fast variable elimination method are developed. They are intuitive, simple to implement and give results which are in very good agreement with those found from numerical simulations. The relative simplicity of the techniques makes them ideal for applying to problems featuring demographic stochasticity, for experts and non-experts alike.
Within the context of mathematical modelling, fast variable elimination is one of the central tools with which one can simplify a multivariate problem. When used in the context of of deterministic systems, the theory is quite standard, but when stochastic effects are present, it becomes less straightforward to apply.
While the introductory and background chapters form an excellent primer to the theory of stochastic population dynamics, the techniques developed can be applied to systems exhibiting a separation of timescales in a variety of fields including population genetics, ecology and epidemiology.

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 In this thesis two variants of the fast variable elimination method are developed. They are intuitive, simple to implement and give results which are in very good agreement with those found from numerical simulations. The relative simplicity of the techniques makes them ideal for applying to problems featuring demographic stochasticity, for experts and non-experts alike.
Within the context of mathematical modelling, fast variable elimination is one of the central tools with which one can simplify a multivariate problem. When used in the context of of deterministic systems, the theory is quite standard, but when stochastic effects are present, it becomes less straightforward to apply.
While the introductory and background chapters form an excellent primer to the theory of stochastic population dynamics, the techniques developed can be applied to systems exhibiting a separation of timescales in a variety of fields including population genetics, ecology and epidemiology.

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