Solution and properties of age population balance models which assume discrete division ages

Abstract

A solution procedure for models of the transient age distribution which employ the assumption of discrete, constant division ages is developed. The solutions for the final state of the age distribution, the solutions obtained in the limit as time goes to infinity, are found to have properties which do not make biological sense. In particular, the solutions will only approach the steady-state solution for very special initial conditions. For most initial conditions, the solution for the final state will instead exhibit an oscillatory behavior. In addition, the oscillatory solutions are unstable with respect to changes in values of the model parameters and solutions with very different periods of oscillation are found arbitrarily close to each other in the parameter space. Models which assume discrete division ages must therefore be used with caution and may be unsuitable as models of autonomous microbial oscillations.