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Compartmental Models of Migratory Dynamics

Published online by Cambridge University Press:  05 October 2011

J. Knisley ,
T. Schmickl  and
I. Karsai
J. Knisley*
Affiliation:
The Institute for Quantitative Biology, East Tennessee State University Mathematics and Statistics, East Tennessee State University, Johnson City, TN 37614 USA
T. Schmickl
Affiliation:
Artificial Life Lab of the Department of Zoology, Karl-Franzens-University
I. Karsai
Affiliation:
The Institute for Quantitative Biology, East Tennessee State University Biological Sciences, East Tennessee State University, Johnson City, TN 37614 USA
*
⋆ Corresponding author. E-mail: knisleyj@etsu.edu
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Abstract

Compartmentalization is a general principle in biological systems which is observable on all size scales, ranging from organelles inside of cells, cells in histology, and up to the level of groups, herds, swarms, meta-populations, and populations. Compartmental models are often used to model such phenomena, but such models can be both highly nonlinear and difficult to work with.

Fortunately, there are many significant biological systems that are amenable to linear compartmental models which are often more mathematically accessible. Moreover, the biology and mathematics is often so intertwined in such models that one can be used to better understand the other. Indeed, as we demonstrate in this paper, linear compartmental models of migratory dynamics can be used as an exciting and interactive means of introducing sophisticated mathematics, and conversely, the associated mathematics can be used to demonstrate important biological properties not only of seasonal migrations but also of compartmental models in general.

We have found this approach to be of great value in introducing derivatives, integrals, and the fundamental theorem of calculus. Additionally, these models are appropriate as applications in a differential equations course, and they can also be used to illustrate important ideas in probability and statistics, such as the Poisson distribution.

Keywords

compartmental modelserlangpoissonexponential
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 6: Biomathematics Education , 2011 , pp. 245 - 259
Copyright
© EDP Sciences, 2011

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