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Propagation of Growth Uncertainty in a PhysiologicallyStructured Population

Published online by Cambridge University Press:  17 October 2012

H.T. Banks  and
S. Hu
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Abstract

In this review paper we consider physiologically structured population models that havebeen widely studied and employed in the literature to model the dynamics of a wide varietyof populations. However in a number of cases these have been found inadequate to describesome phenomena arising in certain real-world applications such as dispersion in thestructure variables due to growth uncertainty/variability. Prompted by this, we describedtwo recent approaches that have been investigated in the literature to describe thisgrowth uncertainty/variability in a physiologically structured population. One involvesformulating growth as a Markov diffusion process while the other entails imposing aprobabilistic structure on the set of possible growth rates across the entire population.Both approaches lead to physiologically structured population models with nontrivialdispersion. Even though these two approaches are conceptually quite different, they werefound in [17] to have a close relationship: in somecases with properly chosen parameters and coefficient functions, the resulting stochasticprocesses have the same probability density function at each time.

Keywords

uncertaintystructured population modelsMarkov diffusion processesItô stochastic differential equationsFokker-Planck equations
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 5: Immunology , 2012 , pp. 7 - 23
Copyright
© EDP Sciences, 2012

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