A mathematical model for the admission process in intensive care units

A mathematical model is given for the admission process in Intensive Care Units (ICUs). It is shown that the model exhibits bistability for certain values of its parameters. In particular, it is observed that in a two-dimensional parameter space, two saddle-node bifurcation curves terminate at a single point of the cusp bifurcation, creating an enclosed region in which the model has one unstable and two stable states. It is shown that in the presence of bistability, variations in the value of parameters may lead to undesired outcomes in the admission process as the value of state variables abruptly changes. Using numerical simulations, it is also discussed how such outcomes can be avoided by appropriately adjusting the parameter values.