# Propagation of Growth Uncertainty in a Physiologically Structured Population

Mathematical Modelling of Natural Phenomena (2012)

- Volume: 7, Issue: 5, page 7-23
- ISSN: 0973-5348

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topBanks, H.T., and Hu, S.. "Propagation of Growth Uncertainty in a Physiologically Structured Population." Mathematical Modelling of Natural Phenomena 7.5 (2012): 7-23. <http://eudml.org/doc/222433>.

@article{Banks2012,

abstract = {In this review paper we consider physiologically structured population models that have
been widely studied and employed in the literature to model the dynamics of a wide variety
of populations. However in a number of cases these have been found inadequate to describe
some phenomena arising in certain real-world applications such as dispersion in the
structure variables due to growth uncertainty/variability. Prompted by this, we described
two recent approaches that have been investigated in the literature to describe this
growth uncertainty/variability in a physiologically structured population. One involves
formulating growth as a Markov diffusion process while the other entails imposing a
probabilistic structure on the set of possible growth rates across the entire population.
Both approaches lead to physiologically structured population models with nontrivial
dispersion. Even though these two approaches are conceptually quite different, they were
found in [17] to have a close relationship: in some
cases with properly chosen parameters and coefficient functions, the resulting stochastic
processes have the same probability density function at each time.},

author = {Banks, H.T., Hu, S.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {uncertainty; structured population models; Markov diffusion processes; Itô stochastic differential equations; Fokker-Planck equations},

language = {eng},

month = {10},

number = {5},

pages = {7-23},

publisher = {EDP Sciences},

title = {Propagation of Growth Uncertainty in a Physiologically Structured Population},

url = {http://eudml.org/doc/222433},

volume = {7},

year = {2012},

}

TY - JOUR

AU - Banks, H.T.

AU - Hu, S.

TI - Propagation of Growth Uncertainty in a Physiologically Structured Population

JO - Mathematical Modelling of Natural Phenomena

DA - 2012/10//

PB - EDP Sciences

VL - 7

IS - 5

SP - 7

EP - 23

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

LA - eng

KW - uncertainty; structured population models; Markov diffusion processes; Itô stochastic differential equations; Fokker-Planck equations

UR - http://eudml.org/doc/222433

ER -

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