Blomhøj, M., T.H. Kjeldsen, and J. Ottesen. 2014. Compartment models. North Carolina State University. 47 pp. http://www4.ncsu.edu~msolufse/Compartmentmodels.pdf . Accessed 15 June 2015.
From the Introduction
"Compartment models are often used to describe transport of material in biological systems. A compartment model contains a number of compartments, each containing well mixed material. Compartments exchange material with each other following certain rules.
"Figure 1.1 shows a sketch of such a system. In this figure, compartments are represented by boxes and the connections between the compartments are represented by arrows. Every compartment (that is every box) has a number of connections leading to the box (inflows) and a number of arrows leading from the box (outflows). Material can either flow from one compartment to another, it can be added from the outside through a source, or it can be removed through a drain or a sink. Think of a bathtub, where water (the well-mixed material) is added through the faucet and leaves through the drain. In the example above,
the material was water, but it can be used in a more abstract way. Generally, the material represents the amount of something that we wish to account for. To account for the material the model must fulfill some conservation law. In the bathtub example, we could develop a model based on conservation of mass. Most compartment models (as the one shown in Figure 1.1) have more than one compartment and equations for such a model are obtained by describing a conservation law for each compartment.
"Material can be stored in the boxes and transported between boxes following arrows. state that the difference between what flows in and what flows out . A compartment model could also represent an ecological system where the material could be energy, the compartments could represent different species of animals and plants, and the flow between compartments could account for uptake and loss of food (or energy). In this case we would base the equations on laws describing conservation of energy. Compartment models also arise in physiology, where the material could be oxygen that is transported with the blood between different organs (compartments) in the body."
The work is rich in illustrations and offers a solid set of references on which readers could build a good inventory of compartment models.
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