Summary
Two conceptually different approaches to incorporate growth uncertainty into size-structured population models have recently been investigated. One entails imposing a probabilistic structure on all the possible growth rates across the entire population, which results in a growth rate distribution model. The other involves formulating growth as a Markov stochastic diffusion process, which leads to a Fokker-Planck model. Numerical computations verify that a Fokker-Planck model and a growth rate distribution model can, with properly chosen parameters, yield quite similar time dependent population densities. The relationship between the two models is based on the theoretical analysis in [7].
This research was supported in part (HTB and SH) by grant number R01AI071915-07 from the National Institute of Allergy and Infectious Diseases, in part (HTB and SH) by the Air Force Office of Scientific Research under grant number FA9550-09-1-0226 and in part (JLD) by the US Department of Energy Computational Science Graduate Fellowship under grant DE-FG02-97ER25308.
On the occasion of the 2009 Festschrift in honor of Chris Byrnes and Anders Lindquist.
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Banks, H.T., Davis, J.L., Hu, S. (2010). A Computational Comparison of Alternatives to Including Uncertainty in Structured Population Models, . In: Hu, X., Jonsson, U., Wahlberg, B., Ghosh, B. (eds) Three Decades of Progress in Control Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11278-2_2
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