Math. Model. Nat. Phenom.
Volume 7, Number 5, 2012Immunology
|7 - 23
|17 October 2012
Propagation of Growth Uncertainty in a Physiologically Structured Population
Center for Research in Scientific Computation, Center
for Quantitative Sciences in Biomedicine North Carolina State
⋆ Corresponding author. E-mail: email@example.com
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  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.
Mathematics Subject Classification: 35Q80 / 60H10 / 60J60 / 92D25
Key words: uncertainty / structured population models / Markov diffusion processes / Itô stochastic differential equations / Fokker-Planck equations
© EDP Sciences, 2012
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