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Propagation of Growth Uncertainty in a Physiologically Structured Population

H.T. Banks; S. Hu

Mathematical Modelling of Natural Phenomena (2012)

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

Abstract

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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.

How to cite

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Banks, 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 -

References

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