Iron is a metal essential for cellular metabolism. However, excess iron available for reactions contributes to the formation of dangerous reactive oxygen species, such as the hydroxyl radical, via the Fenton reaction. Therefore, intracellular iron levels are tightly constrained by a control system of proteins. This paper contains a mathematical model, in the form of a system of five ordinary differential equations, of the core of this control system, including the labile iron pool as well as proteins that regulate uptake, storage, and export and are connected through negative feedback loops. The model is validated using data from an overexpression experiment with cultured human breast epithelial cells. The parameters in the mathematical model are not known for this particular cell culture system, so the analysis of the model was done for a generic choice of parameters. Through a mixture of analytical arguments and extensive simulations it is shown that for any choice of parameters the model reaches a unique stable steady state, thereby ruling out oscillatory behavior. It is shown furthermore that the model parameters are identifiable through suitable experiments.